COUPLED FIXED POINT THEOREMS IN GENERALIZED METRIC SPACES

Year 2011, Volume: 40 Issue: 3, 441 - 447, 01.03.2011

W. Shatanawi

https://izlik.org/JA78FS62YA

Abstract

T. G. Bhaskar and V. Lakshmikantham (Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65, 1379–1393, 2006), V. Lakshmikantham and Lj. B. Ciri´c ( ´ Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis 70, (2009) 4341–4349, 2009) introduced the concept of a coupled coincidence point of a mapping F from X ×X into X and a mapping g from X into X. In the present paper, we prove a coupled coincidence fixed point theorem in the setting of a generalized metric space in the sense of Z. Mustafa and B. Sims.

Keywords

Common fixed Point , Coupled coincidence fixed point , Generalized metric space , 2000 AMS Classification: 54 H 25

COUPLED FIXED POINT THEOREMS IN GENERALIZED METRIC SPACES

https://izlik.org/JA78FS62YA

Abstract

References

• Abbas, M. and Jungck, G. Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341, 416–420, 2008.
• Abbas, M. and Rhoades, B. E. Common fixed point results for noncommuting mapping without continuity in generalized metric spaces, Applied Mathematics and Computation 215, 262–269, 2009.
• Abdeljawad, Th. Completion of cone metric spaces, Hacet. J. Math. Stat. 39,67–74, 2010. [4] Beg, I. and Abbas, M. Coincidence point and invariant approximation for mappings satis- fying generalized weak contractive condition, Fixed Point Theor. Appl., Article ID 74503, 1–7, 2006.
• Bhaskar, T. G and Lakshmikantham, G. V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65, 1379–1393, 2006.
• Haung, L. G. and Zhang, X. Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332, 1468–1476, 2007.
• Jungck, G. Commuting maps and fixed points, Am. Math. Monthly 83, 261–263, 1976.
• Jungck, G. Compatible mappings and common fixed points, Int. J. Math. Sci. 9 (4), 771–779, 1986.
• Jungck, G. Common fixed points for commuting and compatible maps on compacta, Proc. Am. Math. Soc. 103, 977–983, 1988.
• Jungck, G. and Hussain, N. Compatible maps and invariant approximations, J. Math. Anal. Appl. 325 (2), 1003–1012, 2007.
• Lakshmikantham, V. and ´Ciri´c, Lj. B. Coupled fixed point theorems for nonlinear contrac- tions in partially ordered metric spaces, Nonlinear Analysis 70, 4341–4349, 2009.
• P. P. Murthy, P. P. and Tas, K. New common fixed point theorems of Gregus type for R- weakly commuting mappings in 2-metric spaces, Hacet. J. Math. Stat. 38, 285–291, 2009. [13] Mustafa, Z. and Sims, B. Some Remarks concerning D-metric spaces, in: Proc. Int. Conf. on Fixed Point Theor. Appl., Valencia (Spain), July 2003, pp. 189–198.
• Mustafa, Z. and Sims, B. A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2), 289–297, 2006.
• Mustafa, Z., Shatanawi, W. and Bataineh, M. Existence of fixed point results in G-metric spaces, International Journal of Mathematics and Mathematical Sciences Volume, Article ID 283028, 10 pages, 2009.
• Mustafa, Z., Obiedat, H. and Awawdeh, F. Some common fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theor. Appl. Article ID 189870, 12 pages, 2008. [17] Pant, R. P. Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188, 436–440, 1994.
• Popa, V. and Mocanu, M. Altering distance and common fixed points under implicit rela- tions, Hacet. J. Math. Stat. 38, 329–337, 2009.
• Sahin, I. and Telci, M. Fixed points of contractive mappings on complete cone metric spaces, Hacet. J. Math. Stat. 38, 59–67, 2009.
• Sedghi, S., Altun, I. and Shobe, N. Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis 72, 1298–1304, 2010.
• Shatanawi, W. Common fixed point result for two self-maps in G-metric space, submitted. [22] Shatanawi, W. Some fixed point theorems in ordered G-metric spaces and applications, Abstr. Appl. Anal. 2011 (2011), Article ID 126205, 11 pages, doi:10.1155/2011/126205
• Shatanawi, W. Fixed point theory for contractive mappings satisfying Φ-maps in G- metric spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 181650, 9 pages, doi:10.1155/2010/181650
• Shatanawi, W. Some common coupled fixed point results in cone metric spaces, Int. J. Math. Analysis 4 (48), 2381–2388, 2010.