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Some random coupled best proximity points for a generalized ω-cyclic contraction in polish spaces

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Abstrakty
EN
In this paper, we will introduce the concepts of a random coupled best proximity point and then we prove the existence of random coupled best proximity points in separable metric spaces. Our results extend the previous work of Akbar et al. [1].
Rocznik
Tom
Strony
91--105
Opis fizyczny
Bibliogr. 35 poz.
Twórcy
autor
  • Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
autor
  • Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
Bibliografia
  • [1] Akbar F., Kutbi M.A., Shah M.H., Shafqat N., Random coupled and tripled best proximity results with cyclic contraction in metric spaces, J. Nonlinear Sci. Appl., 9(3)(2016), 940-956.
  • [2] Anh T.N., Random equations and applications to general random fixed point theorems, New Zealand J. Math., 41(2011), 17-24.
  • [3] Beg I., Approximation of random fixed points in normed spaces, Nonlinear Anal., 51(8)(2002), 1363-1372.
  • [4] Beg I., Shahzad N., An application of a random fixed point theorem to random best approximation, Arch. Math., (Basel), 74(4)(2000), 298-301.
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  • [8] Ćirić L., Lakshmikantham V., Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces, Stoch. Anal. Appl., 27(6)(2009), 1246-1259.
  • [9] Di Bari C., Suzuki T., Vetro C., Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 9(11)(2008), 3790-3794.
  • [10] Fan K., Extensions of two fixed point theorems of F. E. Browder, Math. Z., 112(1969), 234-240.
  • [11] Gupta A., Rajput S.S., Kaurav P.S., Coupled Best Proximity Point Theorem in Metric Spaces, International Journal of Analysis and Applications, 4(2)(2014), 201-215.
  • [12] Hanš O., Reduzierende zufällige Transformationen, Czechoslovak Math. J., 7(82)(1957), 154-158.
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  • [14] Hussain N., Latif A., Shafqat N., Weak contractive inequalities and compatible mixed monotone random operators in ordered metric spaces, J. Inequal. Appl., 20(2012), 257.
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  • [16] Khan A.R., Hussain N., Yasmin N., Shafqat N., Random coincidence point results for weakly increasing functions in partially ordered metric spaces, Bull. Iranian Math. Soc., 41(2)(2015), 407-422.
  • [17] Kumam P., Fixed point theorem and random fixed point theorem for set-valued non-self mappings, Thai J. Math., 2(2)(2004), 295-307.
  • [18] Kumam P., Random common fixed points of single-valued and multivalued random operators in a uniformly convex Banach space, J. Comput. Anal. Appl., 13(2)(2011), 368-375.
  • [19] Kumam P., Plubtieng S., Some random fixed point theorems for non-self nonexpansive random operators, Turkish J. Math., 30(4)(2006), 359-372.
  • [20] Kumam P., Plubtieng S., The characteristic of noncompact convexity and random fixed point theorem for set-valued operators, Czechoslovak Math. J., 57(132)(1)(2007), 269-279.
  • [21] Kumam W., Kumam P., Some random fixed point theorems for random asymptotically regular operators, Demonstratio Math., 42(1)(2009), 131-141.
  • [22] Kumam W., Kumam P., Random fixed points of multivalued random operators with property (D), Random Oper. Stoch. Equ., 15(2)(2007), 127-136.
  • [23] Kumam W., Kumam P., Random fixed point theorems for multivalued subsequentially limit-contractive maps satisfying inwardness conditions, J. Comput. Anal. Appl., 14(2)(2012), 239-251.
  • [24] Mongkolkeha C., Cho Y.J., Kumam P., Best proximity points for generalized proximal C-contraction mappings in metric spaces with partial orders, J. Inequal. Appl., 94(2013), pages 12.
  • [25] Mongkolkeha C., Cho Y.J.J., Kumam P., Best proximity points for Geraghty’s proximal contraction mappings, Fixed Point Theory Appl., 180(2013), pages 17.
  • [26] Mongkolkeha C., Kumam P., Best proximity point theorems for generalized cyclic contractions in ordered metric spaces, J. Optim. Theory Appl., 155(1)(2012), 215-226.
  • [27] Nashine H.K., Kumam P., Vetro C., Best proximity point theorems for rational proximal contractions, Fixed Point Theory Appl., 95(2013), pages 11.
  • [28] Rockafellar R.T., Measurable dependence of convex sets and functions on parameters, J. Math. Anal. Appl., 28(1969), 4-25.
  • [29] Sanhan W., Mongkolkeha C., Kumam P., Generalized proximal ψ-contraction mappings and best proximity points, Abstr. Appl. Anal., (2012), Art. ID 896912, pages 19.
  • [30] Sintunavarat W., Kumam P., Coupled best proximity point theorem in metric spaces, Fixed Point Theory Appl., 93(2012), pages 16.
  • [31] Suzuki T., Kikkawa M., Vetro C., The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal., 71(7-8)(2009), 2918-2926.
  • [32] Vetro C., Best proximity points: convergence and existence theorems for p-cyclic mappings, Nonlinear Anal., 73(7)(2010), 2283-2291.
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  • [35] Zhu X.-H., Xiao J.-Z., Random periodic point and fixed point results for random monotone mappings in ordered Polish spaces, Fixed Point Theory Appl., (2010), Art. ID 723216, pages 13.
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Bibliografia
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