Fixed point iterations for Prešić-Kannan nonexpansive mappings in product convex metric spaces
References
- [1] D. E. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc., 82 (1981), 423–424.
- [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.
- [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.
- [4] M. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Springer-Verlag, Berlin, Heidelberg, New York, 1999.
- [5] H. Busemann, Spaces with non-positive curvature, Acta Math., 80 (1948), 259–310.
- [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.
- [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.
- [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.
- [9] R. Kannan, Some results on fixed points—IV, Fund. Math. LXXIV (1972), 181–187.
- [10] R. Kannan, Fixed point theorems in reflexive Banach spaces, Proc. Amer. Math. Soc., 38 (1973), 111–118.
- [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.
- [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.
- [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.
- [14] W. R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc., 4 (1953), 506–510.
- [15] M. Păcurar, Iterative Methods for Fixed Point Approximation, PhD Thesis, “Babeş-Bolyai” University, Cluj-Napoca, 2009.
- [16] ——–, A multi-step iterative method for approximating fixed points of Prešić-Kannan operators, Acta Math. Univ. Comenianae, Vol. LXXIX, 1 (2010), 77–88.
- [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.
- [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.
- [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.
- [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.
- [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.
- [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.
- [23] T. Shimizu and W. Takahashi, Fixed points of multivalued mappings in certain convex metric spaces, Topol. Methods Nonlinear Anal., 8 (1996), 197–203.
- [24] P. M. Soardi, Struttura quasi normale e teoremi di punto unito, Rend. Istit. Mat. Univ. Trieste, 4 (1972), 105–114.
- [25] W. Takahashi, A convexity in metric spaces and non-expansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142–149.
DOI: https://doi.org/10.2478/ausm-2018-0005 | Journal eISSN: 2066-7752
Language: English
Page range: 56 - 69
Submitted on: Feb 21, 2017
Published on: Sep 10, 2018
Published by: Sapientia Hungarian University of Transylvania
In partnership with: Paradigm Publishing Services
Publication frequency: 2 times per year
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© 2018 Hafiz Fukhar-ud-din, Vasile Berinde, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.