AN EXTENDED COUPLED COINCIDENCE POINT THEOREM AND RELATED RESULTS

In this paper, we give an extended coupled coincidence point theorem for a mixed g-monotone mapping F:X→X satisfying a weaker contractive condition. As a result of this theorem, we introduce an extended coupled fixed point theorem. We also explain that there exist a relationship between Theorem 2.1 which is our main theorem and Theorem 1.3 introduced by Choudhury et. al. [ Choudhury, BS, Kundu, A: Appl. Math. Lett. 25,6-10(2012) ].

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  • [1] Freiwald R. C., “An introduction to set theory and topology”, Washington University in St. Louis. 2014. 449 pages.
  • [2] Ran ACM, Reurings MCB “A fixed point theorem in partially ordered sets and some applications to matrix equations”, Proc. Am.Math. Soc. 132, 1435-1443, 2004.
  • [3] Nieto JJ, Rodríguez-López R “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations”, Order 22, 223-239, 2005.
  • [4] Ćirić Lj Cakić, N Rajović, Ume J.S. ”Monotone generalized nonlinear contractions in partially ordered metric spaces”, Fixed Point Theory Appl, Article ID 131294, 2008.
  • [5] Choudhury B.S, Kundu A. “(ψ,α,β)-weak contractions in partially ordered metric spaces”, Appl Math Lett, 25, 6—10, 2012.
  • [6] Harjani J., Sadarangani K. “Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations”, Nonlinear Anal. 72(2010), 1188-1197, 2010.
  • [7] Harandi A.A., Emami H. “A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations”, Nonlinear Anal. 72(2010), 2238-2242, 2010.
  • [8] Bhaskar T.G., Lakshmikantham V. “Fixed point theorems in partially ordered metric spaces and applications”, Nonlinear Anal. 65(2006), 1379-1393, 2006.
  • [9] Lakshmikantham V., Ćirić Lj Cakić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces”, Nonlinear Anal. 70(2009), 4341—4349, 2009.
  • [10] Luong N.V., Thuan N.X., “Coupled fixed points in partially ordered metric spaces and application”, Nonlinear Anal. 74(2011), 983—992, 2011.
  • [11] Berinde, V., “Coupled fixed point theorems for ϕ-contractive mixed monotone mappings in partially ordered metric spaces”, Nonlinear Analysis 75 (2012) 3218—3228, 2012.
  • [12] Cho YJ., Rhoades B.E., Saadati R., Samet B., Shantawi W., “Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type”, Fixed Point Theory Appl, 8 (2012), 2012.
  • [13] Cho, Y.J., He G., Huang N.J., “The existence results of coupled quasi-solutions for a class of operator equations”, Bull.Korean Math. Soc. 47, 455-465, 2010.
  • [14] Abbas, M, Sintunavarat, W, Kumam, P: Coupled fixed point in partially ordered G-metric spaces. Fixed Point Theory Appl. 2012, 31 (2012).