Coupled fixed points results for w-compatible maps in symmetric G-metric spaces
Mustafa et. al  generalized the concept of metric space by introducing G-metric space and proved fixed point theorems for mappings satisfying different contractive conditions [see,21-27]. In this article, we introduce the notion of w-compatible maps, b-coupled coincidence points and b-common coupled fixed points for non self maps and obtain fixed point results using these new notions in G-metric spaces. It is worth to mention that our results neither rely on completeness of the space nor the continuity of any mappings involved therein. Also, relevant examples have been cited to illustrate the effectiveness of our results. As an application, we demonstrate the existence of solution of system of non linear integral equations. Our work sets analogues, unifies, generalizes, extends and improves several well known results existing in literature, in particular the recent results of [1-5,8,9,19,20] etc. in the frame work of G-metric spaces.
B. Fisher, Common Fixed Point of Four Mappings. Bull. Inst. of Math. Academia. Sinica. Vol 11, 1983 , pp 103-113.
B. Singh and S. Jain , A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. 301(2005), 439-448.
C. T. Aage and J. N. Salunke, Fixed points for weak contractions in G-metric spaces, Applied Mathematics E-Notes, 12(2012), 23-28.
G. Jungck, Commuting mappings and fixed point, Amer. Math. Monthly, 83 (1976), 261-263.
G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), 771-779.
H. Aydi , B. Samet and C. Vetro , Coupled fixed point results in cone metric spaces for w-compatible mappings , Aydi et al. Fixed Point Theory and Applications 2011, 2011:27.
K. P. R. Rao , I. Altun and S. H. Bindu , Common Coupled Fixed-Point Theorems in Generalized FuzzyMetric Spaces , Hindawi Publishing Corporation Advances in Fuzzy Systems
Volume 2011, Article ID 986748, 6 pages doi:10.1155/2011/986748
M.Abbas, T.Nazir and R. Saadati , Common fixed point results for three maps in generalized metric space , Abbas et al. Advances in Difference Equations 2011, 2011:49.
M. Gugani, M.Aggarwal and R.Chugh , Common Fixed Point Results in G-Metric Spaces and Applications , International Journal of Computer Applications (0975 – 8887) Volume 43–
No.11, April 2012.
Sunny Chauhan, Sumitra and B.D Pant, Coincidence and common fixed point theorems in intutionistic fuzzy metric Spaces, Far East Journal of Mathematical Sciences, to appear.
Sumitra and Fatimah A. Alshaikh Coupled Fixed Point Theorems for a Pair of Weakly Compatible Maps Along with (CLRg) Property in Fuzzy Metric Spaces , International Journal
of Applied Physics and Mathematics, Vol. 2, No. 5, September 2012.
Sumitra and M. Alamgir Khan, CLRg Property for Coupled Fixed Point Theorems in Fuzzy Metric Spaces , International Journal of Applied Physics and Mathematics, Vol. 2, No. 5,
Sumitra , Coupled Fixed Point Theorem for Weakly Compatible Mappings in Intuitionistic Fuzzy Metric Spaces, International Journal of Computer Applications (0975 – 8887) Volume 50– No.23, July 2012.
Sumitra, Gregus type fixed point results for tangential mappings satisfying contractive condition in Fuzzy metric spaces , Advances in fixed point theory to appear soon.
Sumitra , Coupled Fixed Point Theorem for Compatible Maps and its Variants in Fuzzy Metric Spaces , Jorden Journal of Mathematics and Statics: to appear.
Sumitra, CLRg property for Coupled Fixed Point Theorems in Fuzzy Metric Spaces, Fuzzy Sets and System, to appear.
S.N.Mishra, Common fixed points of Compatible mappings in PM-Spaces, Math.Japon 36 (1991) 283-289.
T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: Theory, Methods and Applications, vol.65, no.7, pp. 1379-1393, 2006.
W. Shatanawi , Coupled Fixed Point Theorems in Generalized Metric Spaces, Hacettepe Journal of Mathematics and Statistics Volume 40 (3) (2011), 441 – 447.
W. Shatanawi, Some Fixed Point Theorems in Ordered G-metric Spaces and Applications, Hindawi Publishing Corporation Abstract and Applied Analysis , Volume 2011 , Article ID 126205,11 pages doi 10.1155/2011/126205.
Z. Mustafa and B. Sims, Some remarks concerning D-metric spaces, Proceedings of International Conference on Fixed Point Theory and Applications, pp. 189-198, Yokohama,
Yokohama, Japan, 2004.
Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear Convex Analysis, 7 (2006), 289-297.
Z. Mustafa, H. Obiedat and F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory and Applications, Volume 2008, Article ID
Z. Mustafa, W. Shatanawi and M. Bataineh, Fixed point theorem on uncomplete G-metric spaces, Journal of Mathematics and Statistics, 4 (2008), 196-201.
Z. Mustafa, W. Shatanawi and M. Bataineh, Existence of fixed point results in G-metric spaces, Int. J. of Math. and Math. Sci., Volume 2009, Article ID 283028,
Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory and Applications, Volume 2009, Article ID 917175, doi:
1155 /2009 /917175.
Z. Mustafa and H. Obiedat , A Fixed Point Theorem of Reich in G-Metric Spaces , CUBO A Mathematical Journal Vol.12, No 01, (83–93). March 2010.
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