Common Fixed Point Theorem in G-Metric Space Using Weakly Compatible Mappings

Dr. Shalu Saxena; Dr. Smita Nair

doi:https://doi.org/10.14445/22315373/IJMTT-V12P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 12 | Number 2 | Year 2014 | Article Id. IJMTT-V12P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V12P515

Common Fixed Point Theorem in G-Metric Space Using Weakly Compatible Mappings

Dr. Shalu Saxena, Dr. Smita Nair

Abstract

In this paper we present a common fixed point theorem for self mappings using the concept of weakly compatible mappings.

Keywords

Complete G-metric Space, Weakley compatible mappings.

References

[1] B.C. Dhage. Generalized metric spaces and mapping with fixed points. Bull. Calcutta Math, Soc. 84(1992),329-336.
[2] B. C. Dhage, On generalized metric spaces and topological structure II, Pure Appl. Math. Sci. 40 (1994), 37-41.
[3] B. C. Dhage, A common fixed point principle in D-metric spaces. Bull. Calcutta Math. Soc. 91 (1999), 475-480.
[4] B. C. Dhage, Generalized metric spaces and topological structure. I, Annalele Stiintifice ale Universitatii Al.I. Cuza, (2000).
[5] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Sci., 9 (4) (1986), 771-779.
[6] G. Jungck, Common fixed points for noncontinuous nonself maps on non-metric spaces, far East J.Math.Sci.,4(1996),199-215.
[7] G. Jungck,, B.E. Rhoades, Fixed points for set valued functions without continuity, Indian J, Pure Appl. Math.29(1998),227-238.
[8] M. Abbas, B.E. Rhoades,Common fixed point results for non-commuting mappings without continuity in generalized metric spaces, Appl. Math. Comput. 215 (2009). 262-269.
[9] M. Abbas, T. Nazir, S. Radcnovic, Some periodic point results in generalized metric spaces, Appl. Math. Comput. 217 (2010). 4094-4099.
[10] R. Chugh, T. Kadian, A. Rani, B. E. Rhoades, Property P in G-metric spaces. Fixed Point Theory Appl. 2010 (2010), Article ID 401684.
[11] S. Sessa, On a weak commutativity condition of mappings in fixed point consideration , Publ. Inst. Math. Soc. 32 (1982), 149-153.
[12] S.S. Tomer, D. Singh, M.S. Rathore, Common fixed point theorems via weakly compatible mappings in complete G-metric spaces: Using control functions. Adv. Fixed Point Theory, 4 (2014) No. 2, 245-262
[13] W. Shatanawi, Fixed point theory for contractive mappings satisfying U-maps in G-metric spaces. Fixed Point Theory Appl. 2010 (2010), Article ID 181650.
[14] Z. Mustafa, B. Sims, Some remarks concerning D-metric spaces, in Proceedings of the International Conferences on Fixed Point Theory and Applications, pp. 189-198, Valencia, Spain, July 2003.
[15] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006), 289-297.
[16] Z. Mustafa, H. Obiedat, F Awawdeh, Some fixed Point theorem for mapping on complete G- metric spaces, Fixed Point Theory Appl. 2008 (2008), Article ID 189870.
[17] Z. Mustafa, B, Sims, Fixed point theorems for contractive mapping in complete G -metric spaces, Fixed Point Theory Appl. 2009 (2009), Article ID 917175.
[18] Z. Muilata, W. Shatanawi, M. Bataineh, Existence of fixed point results in G-metric spaces, Int. Math. Math. Sci. 2009 (2009), Article ID 283028.

Citation :

Dr. Shalu Saxena, Dr. Smita Nair, "Common Fixed Point Theorem in G-Metric Space Using Weakly Compatible Mappings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 12, no. 2, pp. 94-101, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V12P515