Document Type: Research Paper

Authors

Department of Mathematics, University of Peshawar, Peshawar, Pakistan

Abstract

In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples. In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples.

Keywords

Main Subjects

[1] M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416-420.

[2] M. Abbas, B. E. Rhoades, Common fixed point results for noncommuting mapping without continuity in generalized metric spaces, Appl. Math. Comput. 215 (2009), 262-269.

[3] H. Aydi, A fixed point theorem for a contractive condition of integral type involving altering distances, Int. J. Nonlinear Anal. Appl. 3 (1) (2012), 42-53.

[4] T. Abdeljawad, Completion of cone metric spaces, Hacet. J. Math. Stat. 39 (2010), 67-74.

[5] Z. Badehian, M. S. Asgari, Integral type fixed point theorems for $alpha$-admissible mappings satisfying ϕ-contractive inequality, Filomat. 30 (12) (2016), 3227-3234.

[6] I. Beg, M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theor. Appl. (2006), Article ID 74503. 7 pages.

[7] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis., 65 (2006), 1379-1393.

[8] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sciences. 29 (9) (2002), 531-536.

[9] L. G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1468-1476.

[10] G. Jungck, Commuting maps and fixed points, Am. Math. Monthly. 83 (1976), 261-263.

[11] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Sci. 9 (4) (1986), 771 -779.

[12] G. Jungck, Common xed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (1988), 977-983.

[13] G. Jungck, N. Hussain, Compatible maps and invariant approximations, J. Math. Anal. Appl. 325 (2) (2007), 1003-1012.

[14] V. Lakshmikantham, L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis. 70 (2009), 4341-4349.

[15] P. P. Murthy, K. Tas, New common fixed point theorems of Gregus type for R-weakly commuting mappings in 2-metric spaces, Hacet. J. Math. Stat. 38 (2009), 285 -291.

[16] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2) (2006), 289-297.

[17] R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), 436-440.

[18] V. Popa, M. Mocanu, Altering distance and common fixed points under implicit relations, Hacet. J. Math. Stat. 38 (2009), 329-337.

[19] H. Rahimi, P. Vetro, G. Soleimani Rad, Coupled fixed-point results for T-contractions on cone metric spaces with applications, Math. Notes. 98 (1) (2015), 158-167.

[20] H. Rahimi, G. Soleimani Rad, Fixed point theory in various spaces, Lambert Academic Publishing (LAP), Germany, 2012.

[21] R. Shah, A. Zada, Some common fixed point theorems of compatible maps with integral type contraction in G-metric spaces, Proceedings of the Institute of Applied Mathematics. 5 (1) (2106), 64-74.

[22] R. Shah, A. Zada and T. Li, New common coupled fixed point results of integral type contraction in generalized metric spaces, J. Anal. Num. Theor. 4 (2) (2106), 145-152.

[23] W. Shatanawi, Coupled fixed point theorems in generalized metric spaces, Hacet. J. Math. Stat. 40 (3) (2011), 441-447.

[24] A. Zada, R. Shah, T. Li, Integral type contraction and coupled coincidence fixed point theorems for two pairs in g-metric spaces, Hacet. J. Math. Stat. 45 (5) (2016), 1475-1484.