FIXED POINT THEOREMS FOR A THIRD POWER TYPE CONTRACTION MAPPINGS IN G-METRIC SPACES

Year 2013, Volume: 42 Issue: 5, 495 - 500, 01.05.2013

Feng Gu Hongqing Ye

Abstract

In this paper, we introduce a new third power type contractive condition in the G-metric spaces, and several new fixed point theorems areestablished in complete G-metric space. The obtained results in thispaper extend the recent relative results.

Keywords

G-metric space , third power type contraction mappings , fixed point.

References

• Chugh, R., Kadian, T., Rani, A., and Rhoades, B. E. Property P in G-metric Spaces, Fixed Point Theory and Applications 2010, Article ID 401684, 2010.
• Dhage, B. C. Generalized metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc. 84, 329–336, 1992.
• Manro, S., Bhatia, S. S. and Kumar, S. Expansion mapping theorems in G-metric spaces, Int. J. Contemp. Math. Sciences 5 No 51, 2529–2535, 2010.
• Mustafa, Z., Awawdeh, F. and Shatanawi, W. Fixed point theorem for expansive mappings in G-metric spaces, Int. J. Contemp. Math. Sciences 5 No 50, 2463–2472, 2010.
• Mustafa, Z., Obiedat, H. and Awawdeh, F. Some fixed point theorems for mappings on complete G-metric spaces, Fixed Point Theory and Applications 2008, Article ID 189870, 200
• Mustafa, Z., Shatanawi, W. and Bataineh, M. Existence of fixed points results in G-metric spaces, International Journal of Mathematics and Mathematical Sciences 2009, Article ID 283028, 2009.
• Mustafa, Z. and Sims, B. Some remarks concerning D-metric spaces, Proceedings of International Conference on Fixed Point Theory and Applications, Yokohama Publishers Valencia Spain, July 13–19, 189–198, 2004.
• Mustafa, Z. and Sims, B. A new approach to a generalized metric space, J. Nonlinear Convex Anal. 7 No 2, 289–297, 2006.
• Mustafa, Z. and Sims,B. Fixed point theorems for contractive mappings in complete Gmetric spaces, Fixed Point Theory and Applications 2009, Article ID 917175, 2009 Shatanawi, W. Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces, Fixed Point Theory and Applications 2010, Article ID 181650, 2010.
• Vats, R. K., Kumar, S. and Sihag, V. Some common fixed point theorem for compatible mappings of type (A) in complete G-metric space, Advances in Fuzzy Mathematics, 6 No 1, 27–38, 2011.