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http://dx.doi.org/10.14317/jami.2014.621

STRONG CONVERGENCE THEOREMS FOR FIXED POINT PROBLEMS OF ASYMPTOTICALLY QUASI-𝜙-NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE  

Jeong, Jae Ug (Department of Mathematics, Dongeui University)
Publication Information
Journal of applied mathematics & informatics / v.32, no.5_6, 2014 , pp. 621-633 More about this Journal
Abstract
In this paper, we introduce a general iterative algorithm for asymptotically quasi-${\phi}$-nonexpansive mappings in the intermediate sense to have the strong convergence in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.
Keywords
fixed point; nonexpansive mapping; asymptotically quasi-${\phi}$-nonexpansive mapping; relatively nonexpansive mapping;
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1 Y.I. Alber, Metric and generalized projection operators in Banach spaces: Properties and applications, in : A. G. Kartosator (Ed.), Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Marcel Dekker, New York, 1996, 15- 50.
2 S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147-150.   DOI   ScienceOn
3 Y.I. Alber, S. Reich, An iterative method for solving a class of nonlinear operator equations in Banach spaces, Panamer. Math. J. 4 (1994), 39-54.
4 B. Halpern, Fixed points of nonexpending maps, Bull. Amer. Math. Soc. 73(1967), 957-961.   DOI
5 Y. Hao, Some results on a modified mann iterative scheme in a reflexive Banach space, Fixed Point Theory Appl. 2013, Article ID 227.
6 W.R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc. 4 (1953), 506-510.   DOI   ScienceOn
7 S. Matsushita and W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory 134 (2005), 257-266.   DOI   ScienceOn
8 K. Nakojo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003), 372-379.   DOI   ScienceOn
9 Y. Su and X. Qin, Strong convergence theorems for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups, Fixed Point Theory Appl. 2006, Article ID 96215.
10 W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000.