On the exsitence and approximation of fixed points of monotone mappings satisfying condition (E) in partially ordered Banach spaces
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Abstract
In this paper, we introduce the notion of a monotone mapping satisfying condition (E) in partially ordered Banach spaces, and establish the exsitence and the approximation of fixed points of such mappings by the Mann iteration process in partially ordered uniformly convex Banach spaces. These results are the generations of the main results in [4, 6, 7]. Also, we provide examples to illustrate the obtained results.
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Keywords
Monotone mapping satisfying condition (E), Mann iteration, partially ordered Banach spaces
References
[1]. K. Aoyama and F. Kohsaka (2011), “Fixed point theorem for a-nonexpansive mapping in Banach space”, Nonlinear Anal., (74), p. 4387-4391.
[2]. M. Bachar and M. A. Khamsi (2015), “On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces”, Fixed Point Theory Appl., (2015:160), p. 1-12.
[3]. B. Beauzamy (1982), Introduction to Banach spaces and their geometry, North-Holland, Amsterdam.
[4]. B. A. B. Dehaish and M. A. Khamsi (2015), “Mann iteration process for monotone nonexpansive mappings”, Fixed Point Theory Appl., (2015:177), p. 1-8.
[5]. E. L. Dozo (1973), “Multivalued nonexpansive mappings and Opial's condition”, Proc. Amer. Math. Soc., 38 (2), p. 286-292.
[6]. J. Garcia-Falset, E. Llorens-Fuster, and T. Suzuki (2011), “Fixed point theory for a class of generalized nonexpansive mappings”, J. Math. Anal. Appl., 375 (1), p. 185-195.
[7]. Y. Song, P. Kumam, and Y. J. Cho (2016), “Fixed point theorems and iterative approximations for monotone nonexpansive mappings in ordered Banach spaces”, Fixed Point Theory Appl., (2016:73), p. 1-11.
[8]. Y. Song, K. Promluang, P. Kumam, and Y. J. Cho (2016), “Some convergence theorems of the Mann iteration for monotone a-nonexpansive mappings”, Appl. Math. Comput., (287-288), p. 74-82.
[9]. W. Takahashi (2000), Nonlinear functional analysis: Fixed point theory and its applications, Yokohama Publishers Inc., Yokohama.
[10]. H. K. Xu (1991), “Inequality in Banach space with applications”, Nonlinear Anal., (16), p. 1127-1138.
[2]. M. Bachar and M. A. Khamsi (2015), “On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces”, Fixed Point Theory Appl., (2015:160), p. 1-12.
[3]. B. Beauzamy (1982), Introduction to Banach spaces and their geometry, North-Holland, Amsterdam.
[4]. B. A. B. Dehaish and M. A. Khamsi (2015), “Mann iteration process for monotone nonexpansive mappings”, Fixed Point Theory Appl., (2015:177), p. 1-8.
[5]. E. L. Dozo (1973), “Multivalued nonexpansive mappings and Opial's condition”, Proc. Amer. Math. Soc., 38 (2), p. 286-292.
[6]. J. Garcia-Falset, E. Llorens-Fuster, and T. Suzuki (2011), “Fixed point theory for a class of generalized nonexpansive mappings”, J. Math. Anal. Appl., 375 (1), p. 185-195.
[7]. Y. Song, P. Kumam, and Y. J. Cho (2016), “Fixed point theorems and iterative approximations for monotone nonexpansive mappings in ordered Banach spaces”, Fixed Point Theory Appl., (2016:73), p. 1-11.
[8]. Y. Song, K. Promluang, P. Kumam, and Y. J. Cho (2016), “Some convergence theorems of the Mann iteration for monotone a-nonexpansive mappings”, Appl. Math. Comput., (287-288), p. 74-82.
[9]. W. Takahashi (2000), Nonlinear functional analysis: Fixed point theory and its applications, Yokohama Publishers Inc., Yokohama.
[10]. H. K. Xu (1991), “Inequality in Banach space with applications”, Nonlinear Anal., (16), p. 1127-1138.
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