On Weakly Commuting Maps and Common Fixed Point Results for Four Maps in G-Metric Spaces ABSTRACT | FULL TEXT

Year 2012, Volume: 41 Issue: 6, 823 - 830, 01.06.2012

W. Shatanawi M. Abbas

Abstract

In this paper, we introduce the concept of weakly commuting maps in G-metric spaces and prove a common fixed point theorem for four self maps in the setting of generalized metric spaces. We also present an example to support our result.

Keywords

Common fixed Point, Weakly Commuting Maps, Generalized Metric Spaces, 2000 AMS Classification: 54 H 25

ON WEAKLY COMMUTING MAPS AND COMMON FIXED POINT RESULTS FOR FOUR MAPS IN G-METRIC SPACES

Abstract

References

• Abbas, M., Nazir, T., Shatanawi W., and Mustafa, Z. Fixed and Related Fixed Point Theorems for Three Maps in G-Metric Spaces, Hacettepe Journal of Mathematics and Statistics 41, 291-306, 2012.
• Abbas, M. and Rhoades, B.E. Common fixed point results for noncommuting mapping without continuity in generalized metric spaces, Appl. Math. and Computation, 215, 262– 269, 2009.
• Aydi, H., Damjanovic, B., Sametc, B. and Shatanawi, W. Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, Math. and Comp. Modelling 54, 2443–2450, 2011.
• Aydi, H., Karapinar, E., and Shatanawi, W. Tripled fixed point results in generalized metric spaces, Journal of Applied Mathematics 2012, Article ID 314279, 10 pages, 2012.
• Aydi, H., Postolache, M., Shatanawi, W. Coupled fixed point results for (ψ, φ)-weakly contractive mappings in ordered G-metric spaces, Computers and Mathematics with Applications 63, 298–309, 2012.
• Chugh, R., Kadian, T., Rani, A. and Rhoades, B. E. Property p in G-metric spaces, Fixed Point Theory Appl. 2010, Article ID 401684, 2010.
• Gholizadeh, L., Saadati, R., Shatanawi, W., and Vaezpour, S. M., Contractive mapping in generalized, ordered metric spaces with application in integral equations, Mathematical Problems in Engineering, Article ID 380784, doi:10.1155/2011/380784, 14 pages, 2011.
• Mustafa, Z. A new structure for generalized metric spaces with application to fixed point theory (Ph.D. Thesis, The University of Newcastle, Australia, 2005).
• Mustafa, Z. and Sims, B. Some remarks concerning D-metric spaces, Proc. Int. Conf. on Fixed Point Theory and Applications, Valencia (Spain), 189–198, 2003.
• Mustafa, Z. and Sims, B. A new approach to generalized metric spaces, J. of Nonlinear and Convex Analysis 7 (2), 289–297, 2006.
• Mustafa, Z., Shatanawi, W. and Bataineh, M. Existence of fixed point results in G-metric spaces, Intl. J. of Math. and Math. Sci. 2009, Article ID 283028, 2009.
• Mustafa, Z., Obiedat, H. and Awawdehand, F. Some fixed point theorem for mapping on complete G- metric spaces, Fixed Point Theory Appl. 2008, Article ID 189870, 2008.
• Saadati, R., Vaezpour, S. M., Vetro, P. and Rhoades, B. E. Fixed point theorems in generalized partially ordered G-metric spaces, Math. and Comp. Modelling 52 (5-6), 797–801, 2010.
• Sessa, S. On a weak commutativity condition of mappings in fixed point consideration, Publ. Inst. Math. Soc. 32, 149–153, 1982.
• Shatanawi, W. Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces, Fixed Point Theory Appl. 2010, Article ID 181650, 2010.
• Shatanawi, W. Coupled fixed point theorems in generalized metric spaces, Hacet. J. Math. Stat. 40 (3), 441–447, 2011.
• Shatanawi, W. Some fixed point theorems in ordered G-metric spaces and applications, Abstr. Appl. Analysis 2011, Article ID 126205, 2011.
• Shatanawi, W. and Postolache, M. Some fixed point results for a G-weak contraction in G-metric spaces, Accepted in Abstract and Applied Analysis.