Fixed Point Type Theorem In S-Metric Spaces (II)

Document Type : Research Articles


Institute of Mathematics, National Academy of Sciences of RA


In this paper, we prove some common fi xed point results for two self mappings
f and g on S-metric space such that f is a g.w.c.m with respect to g.

[1]M. Abbas, A.R. Khan, T. Nazir, Coupled common xed point results in
two generalized metric spaces, Appl. Math. Comput. 217 (2011) 63286336.

[2]M. Abbas, B.E. Rhoades, Common xed point results for noncommuting
mapping without continuity in generalized metric spaces, Appl.
Math.Comput.215 (2009) 262-269.

[3]B.S. Choudhury, Unique xed point theorem for weakly C-contractive
mappings, Kathmandu Univ. J. Sci. Eng. Technol. 5 (1) (2009) 6-13.
[4]S. Gahler, 2-Metrische Raume, and Ihre Topologische Struktur, Math.
Nachr. 26 (1963) 115-148.
[5]S. Gahler, Zur Geometric 2-Metrische Raume, Rev. Roumaine Math.
Pures Appl. 11 (1966) 665-667.
[6]Jungck G and Rhoades B E, Fixed point for set valued functions without
continuity, Indian J. Pure Appl. Math. 29(3) (1998) 227-238
[7]J. Harjani, B. Lopez, K. Sadarangani, Fixed point theorems for weakly Contractive
mappings in ordered metric spaces, Comput. Math. Appl. 61(2011)790-796.
[8]M.S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering
distances between the points, Bull. Aust. Math. Soc. 30 (1984) 1-9.
[9]J.Mojaradi , Some Contractive Mappings On S-Metric Spaces. Math .Theo
.Model 4(14),(2014) 201-210, .
[10]J.Mojaradi , Double Contraction in S-Metric Spaces. International J.
Mathematical Analysis 9(3),(2015) 117-125
[11]Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J.
Nonlinear Convex Anal. 7 (2006) 289-297.
[12]Z. Mustafa, B. Sims, Some remarks concerning D-metric spaces, in Proc.
Int. Conf. on Fixed Point Theory and Applications, Valencia, Spain, July
2003, pp. 189-198.
[13]Z. Mustafa, W. Shatanawi, M. Bataineh, Existence of fixed point results in
G-metric spaces, Int. J. Math. Math. Sci. 2009 (2009) Article ID 283028,
10 pages.
[14]S. Sedghi, N. Shobe, A. Aliouche, A generalization of fi xed point theorem
in S-metric spaces, Mat. Vesnik 64 (2012) 258-266.
[15]W. Shatanawi, M. Abbas, H. Aydi, On weakly C-contractive mappings in
generalized metric spaces (submitted for publication).
[16]W. Shatanawi, Fixed point theorems for nonlinear weakly C-contractive
mappings in metric spaces, Math. Comput. Modeling 54 (2011) 2816-2826.