Fixed point iterations for Prešić-Kannan nonexpansive mappings in product convex metric spaces

[1] D. E. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc., 82 (1981), 423–424.10.1090/S0002-9939-1981-0612733-0Search in Google Scholar

[2] V. Berinde, V. and M. Păcurar, An iterative method for approximating fixed points of Prešić nonexpansive mappings, Rev. Anal. Numér. Théor. Approx., 38 (2) (2009), 144–153.Search in Google Scholar

[3] V. Berinde, A. R. Khan, M. Păcurar, Coupled solutions for a bivariate weakly nonexpansive operator by iterations Fixed Point Theory Appl. 2014, 2014:149, 12 pp.10.1186/1687-1812-2014-149Search in Google Scholar

[4] M. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Springer-Verlag, Berlin, Heidelberg, New York, 1999.10.1007/978-3-662-12494-9Search in Google Scholar

[5] H. Busemann, Spaces with non-positive curvature, Acta Math., 80 (1948), 259–310.10.1007/BF02393651Search in Google Scholar

[6] L. B. Cirić and S. B. Prešić, On Prešić type generalization of the Banach contraction mapping principle, Acta Math. Univ. Comenianae, 76 (2) (2007), 143–147.Search in Google Scholar

[7] H. Fukhar-ud-din, A. R. Khan, Z. Akhtar, Fixed point results for a generalized nonexpansive map in uniformly convex metric spaces, Nonlinear Analysis, 75 (2012) 4747–4760.10.1016/j.na.2012.03.025Search in Google Scholar

[8] H. Fukhar-ud-din, V. Berinde and A. R. Khan, Fixed point approximation of Prešić nonexpansive mappings in product of CAT(0) spaces, Carpatheian J. Math., 32 (3) (2016), 315–322.10.1186/s13663-015-0483-2Search in Google Scholar

[9] R. Kannan, Some results on fixed points—IV, Fund. Math. LXXIV (1972), 181–187.10.4064/fm-74-3-181-187Search in Google Scholar

[10] R. Kannan, Fixed point theorems in reflexive Banach spaces, Proc. Amer. Math. Soc., 38 (1973), 111–118.10.1090/S0002-9939-1973-0313896-2Search in Google Scholar

[11] A. R. Khan, M. A. Khamsi and H. Fukhar-ud-din, Strong convergence of a general iteration scheme in CAT(0)-spaces, Nonlinear Anal., 74 (2011), 783–791.10.1016/j.na.2010.09.029Search in Google Scholar

[12] W. A. Kirk, Geodesic geometry and fixed point theory II, in: Proceedings of the International Conference in Fixed Point Theory and Applications, Valencia, Spain, 2003, pp. 113–142.Search in Google Scholar

[13] M. A. Khamsi and W. A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, Pure and Applied Mathematics. Wiley-Interscience, New York, 2001.10.1002/9781118033074Search in Google Scholar

[14] W. R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc., 4 (1953), 506–510.10.1090/S0002-9939-1953-0054846-3Search in Google Scholar

[15] M. Păcurar, Iterative Methods for Fixed Point Approximation, PhD Thesis, “Babeş-Bolyai” University, Cluj-Napoca, 2009.Search in Google Scholar

[16] ——–, A multi-step iterative method for approximating fixed points of Prešić-Kannan operators, Acta Math. Univ. Comenianae, Vol. LXXIX, 1 (2010), 77–88.Search in Google Scholar

[17] ———, Approximating common fixed points of Prešić-Kannan type operators by a multi-step iterative method, An. Şt. Univ. Ovidius Constan c ta, 17 (1) (2009), pp. 153168.Search in Google Scholar

[18] ———, A multi-step iterative method for approximating common fixed points of Prešić-Rus type operators on metric spaces, Studia Univ. Babeş-Bolyai Math., 55 1 (2010), 149–162.Search in Google Scholar

[19] W. Phuengrattana and S. Suantai, Strong convergence theorems for a countable family of nonexpansive mappings in convex metric spaces, Abstract Applied Anal., vol. 2011, Article ID 929037, 18 pages.10.1155/2011/929037Search in Google Scholar

[20] S. B. Prešić, Sur une classe d’ inéquations aux différences finites et sur la convergence de certaines suites, Publ. Inst. Math. (Beograd)(N.S.), 5(19) (1965), 75–78.Search in Google Scholar

[21] I. Rus, An iterative method for the solution of the equation x = f(x,x,...,x), Rev. Anal. Numer. Theor. Approx., 10 (1) (1981), 95–100.Search in Google Scholar

[22] T. Shimizu, A convergence theorem to common fixed points of families of nonexpansive mappings in convex metric spaces, in Proceedings of the International Conference on Nonlinear and Convex Analysis (2005), 575–585.Search in Google Scholar

[23] T. Shimizu and W. Takahashi, Fixed points of multivalued mappings in certain convex metric spaces, Topol. Methods Nonlinear Anal., 8 (1996), 197–203.10.12775/TMNA.1996.028Search in Google Scholar

[24] P. M. Soardi, Struttura quasi normale e teoremi di punto unito, Rend. Istit. Mat. Univ. Trieste, 4 (1972), 105–114.Search in Google Scholar

[25] W. Takahashi, A convexity in metric spaces and non-expansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142–149.10.2996/kmj/1138846111Search in Google Scholar