Salehi, M., Dadashi, V., Roohi, M. (2010). On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces. Theory of Approximation and Applications, 6(2), 83-91.

M. Salehi; V. Dadashi; M. Roohi. "On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces". Theory of Approximation and Applications, 6, 2, 2010, 83-91.

Salehi, M., Dadashi, V., Roohi, M. (2010). 'On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces', Theory of Approximation and Applications, 6(2), pp. 83-91.

Salehi, M., Dadashi, V., Roohi, M. On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces. Theory of Approximation and Applications, 2010; 6(2): 83-91.

On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces

^{1}Department of Mathematics, Islamic Azad University, Savadkooh Branch, Savadkooh, Iran.

^{2}Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.

^{3}Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran.

Abstract

Some algorithms for nding common xed point of a family of mappings is constructed. Indeed, let C be a nonempty closed convex subset of a uniformly convex Banach space X whose norm is Gateaux dierentiable and let {T_{n}} be a family of self-mappings on C such that the set of all common fixed points of {T_{n}} is nonempty. We construct a sequence {x_{n}} generated by the hybrid method and also we give the conditions of {T_{n}} under which {x_{n}} converges strongly to a common xed point of {T_{n}}.

Article Title [Persian]

On the strong convergence theorems by the hybrid
method for a family of mappings in uniformly
convex Banach spaces

Authors [Persian]

M. Salehi^{1}; V. Dadashi^{2}; M. Roohi^{3}

^{1}Department of Mathematics, Islamic Azad University, Savadkooh Branch, Savadkooh, Iran.

^{2}Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.

^{3}Department of Mathematics, Faculty of Basic Sciences,
University of Mazandaran, Babolsar, Iran.

Abstract [Persian]

Some algorithms for nding common xed point of a family of mappings is constructed. Indeed, let C be a nonempty closed convex subset of a uniformly convex Banach space X whose norm is Gateaux dierentiable and let {T_{n}} be a family of self-mappings on C such that the set of all common fixed points of {T_{n}} is nonempty. We construct a sequence {x_{n}} generated by the hybrid method and also we give the conditions of {T_{n}} under which {x_{n}} converges strongly to a common xed point of {T_{n}}.

Keywords [Persian]

Hybrid method، Common xed point، Iterative algorithm، Uniformly con-
vex Banach space

References

[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{ 379. [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, 2000. [11] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. (TMA) 16 (1991), 1127{1138.