2010
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On The Perimeter of an Ellipse
On The Perimeter of an Ellipse
2
2
Let E be the ellipse with major and minor radii a and b respectively, and Pbe its perimeter, then
P = lim 4 tan(p/n)(a + b + 2) Σ a2 cos2 (2k-2)Pi/n+ sin2 (2k-2)Pi/n;
where n = 2m. So without considering the limit, it gives a reasonable approxi-mation for P, it means that we can choose n large enough such that the amountof error be less than any given small number. On the other hand, the formulasatises both limit status b→a and b→0 which give respectively P = 2a andP = 4a.
1
Let E be the ellipse with major and minor radii a and b respectively, and Pbe its perimeter, then
P = lim 4 tan(p/n)(a + b + 2) Σ a2 cos2 (2k-2)Pi/n+ sin2 (2k-2)Pi/n;
where n = 2m. So without considering the limit, it gives a reasonable approxi-mation for P, it means that we can choose n large enough such that the amountof error be less than any given small number. On the other hand, the formulasatises both limit status b→a and b→0 which give respectively P = 2a andP = 4a.
1
6
A.
Ansari
A.
Ansari
Department of Mathematics, Islamic Azad University, Gachsaran-Branch, Gachsaran, Iran.
Department of Mathematics, Islamic Azad University
Iran
ansari.moh@gmail.com
[[1] Gerard P. Michon, www.numericana.com/answer/ellipse.htm##[2] Gerald B. Folland, Real Analysis, Modern Techniques And Their Applications,##John Wiley And Sons, Second Edition.##[3] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, Third Edition##[4] George B. Thomas, Ross L. Finney Calculus And Analytic Geometry, Addison-##Wesley, Ninth Edition.##]
Redened (anti) fuzzy BM-algebras
Redened (anti) fuzzy BM-algebras
2
2
In this paper by using the notiαon of anti fuzzy points and its besideness to andnon-quasi-coincidence with a fuzzy set the concepts of an anti fuzzy subalgebrasin BM-algebras are generalized and their inter-relations and related propertiesare investigated.
1
In this paper by using the notiαon of anti fuzzy points and its besideness to andnon-quasi-coincidence with a fuzzy set the concepts of an anti fuzzy subalgebrasin BM-algebras are generalized and their inter-relations and related propertiesare investigated.
7
21
A.
Borumand-Saeid
A.
Borumand-Saeid
Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran.
Department of Mathematics, Islamic Azad University
Iran
arsham@mail.uk.ac.ir
[[1] S. A. Bhatti, M. A. Chaudhry and B. Ahmad, On classication of BCI-algebras,##Math. Jap. 34 (1989), 865{876.##[2] S. K. Bhakat and P. Das, (2;2 _ q)-fuzzy subgroup,Fuzzy Sets and Systems 80##(1996), 359{368.##[3] A. Borumand Saeid, Fuzzy BM-algebras, Indian J. Sci. Technol. 3 (2010), 523{##[4] Q. P. Hu and X. Li, On BCH-algebras, Math. Seminar Notes 11 (1983), 313{320.##[5] Q. P. Hu and X. Li, On proper BCH-algebras, Math. Japonica 30 (1985), 659{##[6] K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Math.##Japonica 23 (1978), 1{26.##[7] K. Iseki, On BCI-algebras, Math. Seminar Notes 8 (1980), 125{130.##[8] C. B. Kim and H. S. Kim, On BM-algebras, Sci. Math. Japo. Online e-2006##(2006), 215{221.##[9] H. S. Kim, Y. H. Kim and J. Neggers, Coxeters and pre-Coxeter algebras in##Smarandache setting, Honam Math. J. 26 (2004), 471{481.##[10] Y. B. Jun, On (; )-fuzzy subalgebras of BCI=BCK-algebras, Bull. Korean##Math. Soc. 42 (2005), 703{711.##[11] Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Sci. Math. Japonica##Online 1 (1998), 347{354.##[12] J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa, Co., Seoul, 1994.##[13] J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca 49 (1999), 19{26.##[14] J. Neggers and H. S. Kim, On B-algebras, Mate. Vesnik 54 (2002), 21{29.##[15] J. Neggers and H. S. Kim, A fundamental theorem of B-homomorphism for B-##algebras, Int. Math. J. 2 (2002), 215{219.##[16] A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971), 512-517.##[17] A. Walendziak, Some axiomatizations of B-algebras, Math. Slovaca 56 (2006),##[18] A. Walendziak, A note on normal subalgebras in B-algebras, Sci. Math. Jap.##Online e-2005 (2005), 49{53.##[19] L. A. Zadeh, Fuzzy Sets, Inform. Control 8 (1965), 338{353.##]
BMO Space and its relation with wavelet theory
BMO Space and its relation with wavelet theory
2
2
The aim of this paper is a) if Σak2 < ∞ then Σak rk(x) is in BMO that{rk(x)} is Rademacher system. b) P1k=1 ak!nk (x) 2 BMO; 2k nk < 2k+1that f!n(x)g is Walsh system. c) If jakj < 1k then P1k=1 ak!k(x) 2 BMO.
1
The aim of this paper is a) if Σak2 < ∞ then Σak rk(x) is in BMO that{rk(x)} is Rademacher system. b) P1k=1 ak!nk (x) 2 BMO; 2k nk < 2k+1that f!n(x)g is Walsh system. c) If jakj < 1k then P1k=1 ak!k(x) 2 BMO.
23
28
M.
Ghanbari
M.
Ghanbari
Department of Mathematics, Islamic Azad University, Farahan-Branch, Farahan, Iran.
Department of Mathematics, Islamic Azad University
Iran
m.ghanbari@iau-farahan.ac.ir
[[1] L. Grafakos, Modern Fourier Analysis, Second Edition, Graduate Texts in Math.,##No. 250, Springer, New York, 2008.##[2] L. Grafakos, L. Liu, D. Yang, Maximal function characterizations of Hardy spaces##on RD-spaces and their applications, Sci. China Ser. A 51 (2008), 2253-2284.##[3] Dziubanski, G. Garrigos, T. Martnez, J. L. Torrea, J. Zienkiewicz, BMO spaces##related to Schrodinger operators with potentials satisfying a reverse Holder in-##equality, Math. Z. 249 (2005), 329-356.##[4] E. Hernftndez, G. Weiss, A First Course on wavelet, University Autonoma of##Madrid, Washington University in St. Louis, 1996##[5] B. S. Kashin, A. A. Saakyan, Orthogonal Series, Transl. Mth. Monographs, vol##75, AMS, Providence, 1989##[6] E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and##Oscillatory Integrals, Princeton University Press, Princeton, New Jersey 1993##[7] M. T. Lacey, E. Terwilleger, B. D. Wick, Remarks on product VMO, Proc. Amer.##Math. Soc. 134 (2006), 465-474.##[8] O. Blasco, S. Pott, Dyadic BMO on the bidisk, Rev. Mat. Iberoamericana 21##(2005), , 483-510.##]
Influence of using the strategy of concept maps in learning fractions
Influence of using the strategy of concept maps in
learning fractions
2
2
This paper is about concept maps and how they can assist in the learning ofconcepts of mathematics. First the paper presents the theoretical backgroundand working denitions for concept maps. Then this study examines the impactof using concept maps in learning of fractions. Results of this study indicatedthat using this strategy was eective in learning of fractions for fourth-gradestudents. This result conrms the eectiveness of the strategy of concept mapsin teaching because it includes activities that link the concepts to help studentsunderstand new concepts and link them to previous ones.
1
This paper is about concept maps and how they can assist in the learning ofconcepts of mathematics. First the paper presents the theoretical backgroundand working denitions for concept maps. Then this study examines the impactof using concept maps in learning of fractions. Results of this study indicatedthat using this strategy was eective in learning of fractions for fourth-gradestudents. This result conrms the eectiveness of the strategy of concept mapsin teaching because it includes activities that link the concepts to help studentsunderstand new concepts and link them to previous ones.
29
37
M.
Haghverdi
M.
Haghverdi
Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran.
Department of Mathematics, Islamic Azad University
Iran
m-haghverdi@iau-arak.ac.ir
[[1] J. D. Novak. Concept maps and vee diagrams: Two meta cognitive tools to##facilitate meaningful learning. International Science 19 29-52, (1990).##[2] F. Guastello, Concept mapping eects on science content comprehension of low-##achieving inner-city seventh grades. Remedial and Special Education 21 (2000),##[3] J. M. Kinchin, Using concept maps to reveal understanding: A two-tier analysis.##School Science Review 81 (2000), 41-46.##[4] S. Rashwan, The eect of using concept maps in teaching biology to high school##students and their attitudes towards it. Journal of college of education, Zagazig##University (), 422-454.##[5] S. Gurganus, Math instruction for students with learning problems, Pearson Ed-##ucation Inc. Press.##[6] J. Monagham and E. Bingobali, Concept image revisited, Educational Studies in##Mathematics 68 (2008), 19-35.##[7] L. A. Bolte, Using concept maps and interpretive essays for assessment in math-##ematics. School Science and Mathematics bf 99 (1999), 19-28.##[8] C. Chiou, The eect of concept mapping on students' learning achievements##and interests, Innovations in Education and Teaching Internationa, 45 (2008),##[9] S. K. Wilcox and M. Sahlo, Another perspective on concept maps: Empovering##students, Mathematics Teaching in the Middle School 3 (1998), 464-469.##[10] D. T. Weinhott, Concept mapping by pre service elementary teachers: A case##study of the eect in an integrated methods courses, D. A. I 56 (), 1362-1369. ##[11] P. B. Harton et. al, An investigation of the eectiveness of concept mapping as##an instructional tool,Science Education 77 (1993), 95-110.##[12] K. Hasemann and H. Manseld, Concept mapping in the research on mathe-##matical developmat: back ground, methods nding and conclusions,Educational##Studies in Mathematics 29 (1995), 45-72.##]
Hybrid model in network DEA
Hybrid model in network DEA
2
2
Traditional DEA models deal with measurements of relative eciency ofDMUs regarding multiple - inputs VS. multiple-outputs. One of the drawbacksof these model is the neglect of intermediate products or linkong activities. Af-ter pointing out needs for inclusion of them to DEA models. We propose hybridmodel that can deal with intermediate products formally using this model wecan evaluate divisional eciency of decision making units (DMU) and we showthis model with an example.
1
Traditional DEA models deal with measurements of relative eciency ofDMUs regarding multiple - inputs VS. multiple-outputs. One of the drawbacksof these model is the neglect of intermediate products or linkong activities. Af-ter pointing out needs for inclusion of them to DEA models. We propose hybridmodel that can deal with intermediate products formally using this model wecan evaluate divisional eciency of decision making units (DMU) and we showthis model with an example.
39
44
A.
Jahanshahloo
A.
Jahanshahloo
Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran
[[1] Network DEA: A slack - based measure approach by Kaoru Tone, Miki Tsutsui.##[2] Data Envelopment Analysis by Dr. Gr. Jahanshahloo, Dr. F. Hosseinzadeh Lot,##Dr. H. Nikomaram.##]
Input congestion, technical ineciency and output reduction in fuzzy data envelopment analysis
Input congestion, technical ineciency and output
reduction in fuzzy data envelopment analysis
2
2
During the last years, the concept of input congestion and technical ineff-ciency in data envelopment analysis (DEA), have been investigated by manyresearchers. The motivation of this paper is to present models which obtain thedecreased output value due to input congestion and technical ineciency. More-over, we extend the models to estimate input congestion, technical ineciencyand output reduction in fuzzy data envelopment analysis, by using the conceptof α-cut sets.
1
During the last years, the concept of input congestion and technical ineff-ciency in data envelopment analysis (DEA), have been investigated by manyresearchers. The motivation of this paper is to present models which obtain thedecreased output value due to input congestion and technical ineciency. More-over, we extend the models to estimate input congestion, technical ineciencyand output reduction in fuzzy data envelopment analysis, by using the conceptof α-cut sets.
45
60
M.
khodabakhshi
M.
khodabakhshi
Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran.
Department of Mathematics, Faculty of Science,
Iran
mkhbakhshi@yahoo.com
N.
Aryavash
N.
Aryavash
Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran.
Department of Mathematics, Faculty of Science,
Iran
k.aryavash@yahoo.com
[[1] M. Asgharian, M. Khodabakhshi, L. Neralic, Congestion in stochastic data envelopment##analysis: An input relaxation approach, International Journal of##statistic and Management System, 5 (2010), 84{106. ##[2] R. D. Banker, A. Charnes, W. W. Cooper, Some models for estimating technical##and scale ineciencies in data envelopment analysis, Management Science 30##(1984), 1078{1092.##[3] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the eciency of DMUs,##European Journal of Operational Research 2 (1978), 429-444.##[4] W. W. Cooper, R. G. Thompson, R. M. Thrall, Introduction: Extensions and##new developments in DEA, Annals of Operations Research 66 (1996), 3{46.##[5] W. W. Cooper, L. M. Seiford, J. Zhu, A unied additive model approach for##evaluating ineciency and congestion with associated measures in DEA, Socio-##Economic Planning Sciences 34 (2000), 1{25.##[6] W. W. Cooper, H. Deng, B. Gu, Sh. Li, R. M. Thrall, Using DEA to improve##the management of congestion in Chinese industries, Socio-Economic Planning##Sciences 35 (2001), 227{242.##[7] W. W. Cooper, B. Gu, Sh. Li, Comparisons and evaluations of alternative approaches##to the treatment of congestion in DEA, European Journal of Operational##Research 132 (2001), 62{74.##[8] W. W. Cooper, B. Gu, Sh. Li, Note: Alternative treatments of congestion##in DEA-A response to the cherchye, Kuosmanen and Post critique, European##Journal of Operational Research 132 (2001), 81{87.##[9] W. W. Cooper , L. M. Seiford, J. Zhu. (2001). Slacks and congestion: Response##to a comment by R. Fare and S. Grosskopf, Socio-Economic Planning Sciences##35 (2001) 205-215.##[10] W. W. Cooper, H. Deng, Zh. M. Huang, S. X. Li A one-model approach to##congestion in data envelopment analysis, Socio-Economic Planning Sciences 36##(2002), 231{238.##[11] R. Fare, L. Svensson, Congestion of factors of production, Econometrica 48##(1980), 1743{1753.##[12] R. Fare, S. Groskopf, Measuring congestion in production, Zeitschrift fur Na-##tionalokonomie 43 (1983), 257-271.##[13] R. Fare, S. Groossko, When can slacks be used to identify congestion? An##answer to W. W. Cooper, L. Seiford and J. Zhu, Socio-Economic Planning##Sciences 35 (2001), 217{221.##[14] G. R. Jahanshahloo, M. Khodabakhshi, Suitable combination of inputs for improving##outputs in DEA with determining input congestion-Considering textile##industry of China, Applied Mathematics and Computation 151 (2004), 263{273. ##[15] G. R. Jahanshahloo, M. Khodabakhshi, Determining assurance interval for non-##Archimedean element in the improving outputs model in DEA, Applied Mathe-##matics and Computation 151 (2004), 501{506.##[16] M. Khodabakhshi, A one-model approach based on relaxed combinations of##inputs for evaluating input congestion in DEA, Journal of Computational and##Applied mathematics 230 (2009) ,443{450.##[17] M. Khodabakhshi, Estimating most productive scale size with stochastic data##in data envelopment analysis, Economic Modelling 26 (2009), 968-973.##[18] M. Khodabakhshi, M. Asgharian, An input relaxation measure of eciency in##stochastic data envelopment analysis, Applied Mathematical Modelling 33 (2009),##2010-2023.##[19] M. S. Saadati, A. Memariani, Reducing weight exibility in fuzzy DEA, Applied##Mathematicsand Computation 161 (2005), 611{622.##[20] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets System##1 (1978), 3{28.##]
Some notes concerning the convergence control parameter in homotopy analysis method
Some notes concerning the convergence control
parameter in homotopy analysis method
2
2
omotopy analysis method (HAM) is a promising method for handling func-tional equations. Recent publications proved the eectiveness of HAM in solvingwide variety of problems in dierent elds. HAM has a unique property whichmakes it superior to other analytic methods, this property is its ability to con-trol the convergence region of the solution series. In this work, we claried theadvantages and eects of convergence-control parameter through an example.
1
omotopy analysis method (HAM) is a promising method for handling func-tional equations. Recent publications proved the eectiveness of HAM in solvingwide variety of problems in dierent elds. HAM has a unique property whichmakes it superior to other analytic methods, this property is its ability to con-trol the convergence region of the solution series. In this work, we claried theadvantages and eects of convergence-control parameter through an example.
61
72
M.
Paripour
M.
Paripour
Department of Mathematics, Islamic Azad University, Hamedan Branch , Hamedan, 6518118413,
Iran.
Department of Mathematics, Islamic Azad University
Iran
m paripour@yahoo.com
J.
Saeidian
J.
Saeidian
Department of Mathematics and Computer Science, Tarbiat Moallem University, 599 Taleghani
avenue, Tehran 1561836314, Iran.
Department of Mathematics and Computer Science,
Iran
[[1] S. Abbasbandy, Homotopy analysis method for heat radiation equations, Int.##Commun. Heat Mass Transf. 34 (2007), 380{387.##[2] S. Abbasbandy, The application of the homotopy analysis method to nonlinear##equations arising in heat transfer, Phys. Lett. A 360 (2006) 109-113.##[3] S. Abbasbandy, F. Samadian Zakaria, Soliton solutions for the 5th-order KdV##equation with the homotopy analysis method, Nonlinear Dyn. 51 (2008) 83{87.##[4] S. Abbasbandy, Y. Tan and S. J. Liao, Newton-homotopy analysis method for##nonlinear equations, Appl. Math. Comput. 188 (2007), 1794{1800.##[5] T. Hayat, T. Javed, M. Sajid, Analytic solution for rotating ow and heat transfer##analysis of a third-grade uid, Acta Mech 191 (2007), 219{229.##[6] T. Hayat, M. Sajid, Homotopy analysis of MHD boundary layer ow of an upper-##convected Maxwell uid, Int. J. Eng. Sci. 45 (2007), 393{401.##[7] T. Hayat, M. Sajid, Analytic solution for axisymmetric ow and heat transfer##of a second grade uid past a stretching sheet, Int. J. Heat Mass Transfer, 50##(2007), 75{84. ##[8] M. Inc, On exact solution of Laplace equation with Dirichlet and Neumann##boundary conditions by the homotopy analysis method, Phys. Lett. A 365 (2007),##[9] S. J. Liao, Proposed homotopy analysis technique for the solution of nonlinear##problems, Ph.D. dissertation, Shanghai Jiao Tong University, 1992.##[10] S. J. Liao, A kind of approximate solution technique which does not depend upon##small parameters: a special example, Int. J. of Non-Linear Mech. 30 (1995),##[11] S. J. Liao, A kind of approximate solution technique which does not depend upon##small parameters (II): an application in uid mechanics, Int. J. of Non-Linear##Mech. 32 (1997) 815{822.##[12] S. J. Liao, A. T. Chwang, Application of homotopy analysis method in nonlinear##oscillations, ASME. J. of Appl. Mech. 65 (1998), 914{922.##[13] S. J. Liao, Beyond perturbation: An introduction to homotopy analysis method,##Chapman Hall/CRC Press, Boca Raton, 2003.##[14] S. J. Liao, On the relationship between the homotopy analysis method and Euler##transform, Commun. Nonlin. Sci. Num. Simul. 18 (2010), 1421-1431.##[15] S. J. Liao, E. Magyari, Exponentially decaying boundary layers as limiting cases##of families of algebraically decaying ones, ZAMP 57 (2006), 777{792.##[16] S. J. Liao, A new branch of solutions of boundary-layer ows over a permeable##stretching plate, Int. J. Non-Linear Mech. 42 (2007), 819{830.##[17] S. J. Liao, Notes on the homotopy analysis method: Some denitions and theo-##rems, Commun. Nonlin. Sci. Num. Simul. 14 (2009) 983{997.##[18] S. J. Liao, An optimal homotopy analysis approach for strongly nonlinear dier-##ential equations, Commun. Nonlin. Sci. Num. Simul. 15 (2010), 2003{2016.##[19] Y. P. Liu, Z. B. Li, The homotopy analysis method for approximating the solution##of the modied Korteweg-de Vries equation, Chaos, Solitons and Fractals, 39##(2009), 1{8.##[20] M. Paripour, E. Babolian, J. Saeidian, Analytic solutions to diusion equations,##Math. Comput. Mod. 51 (2010), 649{657.##[21] M. Sajid, T. Hayat, S. Asghar, Comparison between the HAM and HPM solutions##of thin lm ows of non-Newtonian uids on a moving belt, Nonlinear Dyn. 50##(2007), 27{35.##[22] Z. Wang, L. Zou, H. Zhang, Applying homotopy analysis method for solving##dierential-dierence equation, Phys. Lett. A 369 (2007), 77{84. ##[23] S. P. Zhu, An exact and explicit solution for the valuation of American put##options, Quantitative Finance 6 (2006), 229{242.##[24] S. P. Zhu, A closed-form analytical solution for the valuation of convertible bonds##with constant dividend yield, ANZIAM J. 47 (2006), 477{494.##[25] L. Zou, Z. Zong, Z. Wang, L. He, Solving the discrete KdV equation with homo-##topy analysis method, Phys. Lett. A 370 (2007), 287{294.##]
A numerical solution of Nagumo telegraph equation by Adomian decomposition method
A numerical solution of Nagumo telegraph equation
by Adomian decomposition method
2
2
In this work, the solution of a boundary value problem is discussed via asemi analytical method. The purpose of the present paper is to inspect theapplication of the Adomian decomposition method for solving the Nagumo tele-graph equation. The numerical solution is obtained for some special cases sothat demonstrate the validity of method.
1
In this work, the solution of a boundary value problem is discussed via asemi analytical method. The purpose of the present paper is to inspect theapplication of the Adomian decomposition method for solving the Nagumo tele-graph equation. The numerical solution is obtained for some special cases sothat demonstrate the validity of method.
73
81
H.
Rouhparvar
H.
Rouhparvar
Department of Mathematics, Islamic Azad University, Saveh-Branch, Saveh 39187/366, Iran.
Department of Mathematics, Islamic Azad University
Iran
rouhparvar59@gmail.com
[[1] T. A. Abassy, Improved Adomian decomposition method, Comput. Math. Appl.##9 (2010), 42{54.##[2] S. Abbasbandy, Soliton solutions for the Fitzhugh-Nagumo equation with the##homotopy analysis method, Appl. Math. Model., 32 (2008), 2706{2714.##[3] S. Abbasbandy, A Numerical solution of Blasius equation by Adomian's decom-##position method and comparison with homotopy perturbation method, Chaos,##Solitons and Fractals, 31 (2007), 257{260.##[4] S. Abbasbandy, Improving Newton-Raphson method for nonlinear equations by##modied Adomian decomposition method, Appl. Math. Comput. 145 (2004),##[5] S. Abbasbandy, M.T. Darvish, A numerical solution of Burger's equation by##modied Adomian method, Appl. Math. Comput. 163 (2005), 1265{1272.##[6] H.A. Abdusalam, E.S. Fahmy, Cross-diusional eect in a telegraph reaction##diusion Lotka-Volterra two competitive system, Chaos, Solitons & Fractals, 18##(2003), 259{264.##[7] H. A. Abdusalam, Analytic and approximate solutions for Nagumo telegraph##reaction diusion equation, Appl. Math. Comput. 157 (2004), 515{522. ##[8] G. Adomain, Solving frontier problems of physics: The decomposition method,##Kluwer Academic Publishers, Boston, 1994.##[9] G. Adomian, Nonlinear stochastic operator equations, Academic Press, 1986.##[10] G. Adomian, A review of the decomposition method in applied mathematics, J.##Math. Anal. Appl. 135 (1998), 501{544.##[11] G. Adomian, Y. Charruault, Decomposition method-A new proof of convergency,##Math. Comput. Model. 18 (1993), 103{106.##[12] E. Ahmed, H. A. Abdusalam, E. S. Fahmy, On telegraph reaction diusion and##coupled map lattice in some biological systems, Int. J. Mod. Phys C, 2 (2001),##[13] E. Babolian, J. Biazar, Solution of a system of nonlinear Volterra integral equa-##tions by Adomian decomposition method, Far East J. Math. Sci. 2 (2000), 935{##[14] E. Babolian, Sh. Javadi, H. Sadeghi, Restarted Adomian method for integral##equations, Appl. Math. Comput. 153 (2004), 353{359.##[15] S. A. El-Wakil, M. A. Abdou, New applications of Adomian decomposition##method, Chaos, Solitons and Fractals 33 (2007), 513{522.##[16] A. C. Metaxas, R. J. Meredith, Industrial microwave, heating, Peter Peregrinus,##London, 1993.##[17] N. Ngarhasts, B. Some, K. Abbaoui, Y. Cherruault, New numerical study of##Adomian method applied to a diusion model, Kybernetes 31 (2002), 61{75.##[18] W. Liu, E. Van Vleck, Turning points and traveling waves in FitzHugh-Nagumo##type equations, J. Di. Eq. 2 (2006), 381{410.##[19] G. Roussy, J. A. Pearcy, Foundations and industrial applications of microwaves##and radio frequency elds, John Wiley, New York, 1995.##[20] R. A. Van Gorder, K. Vajravelu, A variational formulation of the Nagumo##reaction-diusion equation and the Nagumo telegraph equation, Nonlinear Anal-##ysis: Real World Applications 4 (2010), 2957{2962.##[21] A.W. Wazwaz, A reliable modication of Adomian decomposition method, Appl.##Math. Comput. 102 (1999), 77{86.##[22] A. M. Wazwaz, A new algorithm for calculating Adomian polynomials for non-##linear operators, Appl. Math. Comput. 111 (2000), 53{69.##]
On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces
On the strong convergence theorems by the hybrid
method for a family of mappings in uniformly
convex Banach spaces
2
2
Some algorithms for nding common xed point of a family of mappings isconstructed. Indeed, let C be a nonempty closed convex subset of a uniformlyconvex Banach space X whose norm is Gateaux dierentiable and let {Tn} bea family of self-mappings on C such that the set of all common fixed pointsof {Tn} is nonempty. We construct a sequence {xn} generated by the hybridmethod and also we give the conditions of {Tn} under which {xn} convergesstrongly to a common xed point of {Tn}.
1
Some algorithms for nding common xed point of a family of mappings isconstructed. Indeed, let C be a nonempty closed convex subset of a uniformlyconvex Banach space X whose norm is Gateaux dierentiable and let {Tn} bea family of self-mappings on C such that the set of all common fixed pointsof {Tn} is nonempty. We construct a sequence {xn} generated by the hybridmethod and also we give the conditions of {Tn} under which {xn} convergesstrongly to a common xed point of {Tn}.
83
91
M.
Salehi
M.
Salehi
Department of Mathematics, Islamic Azad University, Savadkooh Branch, Savadkooh, Iran.
Department of Mathematics, Islamic Azad University
Iran
msalehi76@yahoo.com
V.
Dadashi
V.
Dadashi
Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.
Department of Mathematics, Islamic Azad University
Iran
vahid.dadashi@iausari.ac.ir
M.
Roohi
M.
Roohi
Department of Mathematics, Faculty of Basic Sciences,
University of Mazandaran, Babolsar, Iran.
Department of Mathematics, Faculty of Basic
Iran
mehdi.roohi@gmail.com
[[1] S. Atsushiba and W. Takahashi, Strong convergence theorems for nonexpansive##semigroups by a hybrid method, J. Nonlinear Convex Anal. 3 (2002), 231{242.##[2] H. H. Bauschke and P. L. Combettes, A weak-to-strong convergence principle for##fejer-monotone methods in Hilbert spaces, Math. Oper. Res. 26 (2001), 248{264.##[3] K. Goebel and S. Reich, Uniform convexity, hyperbolic geometry, and nonexpan-##sive mappings, Marcel Dekker, New York, 1984.##[4] Y. Haugazeau, Sur les inequations variationnelles et la minimisation de fonc-##tionnelles convexes, Universite de Paris, Paris, France, 1968.##[5] H. Iiduka, W. Takahashi and M. Toyoda, Approximation of solutions of varia-##tional inequalities for monotone mappings, Panamer. Math. J. 14 (2004), 49{61.##[6] K. Nakajo, K. Shimoji and W. Takahashi, Strong convergence theorems by the##hybrid method for families of mappings in Banach spaces, Nonlinear Anal.(TMA)##71 (2009), 812{818.##[7] K. Nakajo, K. Shimoji and W. Takahashi, Strong convergence theorems by the##hybrid method for families of nonexpansive mappings in Hilbert spaces, Taiwanese##J. Math. 10 (2006), 339{360.##[8] K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive##mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003), 372{##[9] M. V. Solodov and B. F. Svaiter, Forcing strong convergence of proximal point##iterations in a Hilbert space, Math. Program. Ser. A 87 (2000), 189{202.##[10] W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama,##[11] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal.##(TMA) 16 (1991), 1127{1138.##]