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http://dx.doi.org/10.7858/eamj.2012.042

ON ASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS IN ARBITRARY BANACH SPACES  

Rafiq, Arif (Hajvery University)
Lee, Byung Soo (Department of Mathematics, Kyungsung University)
Publication Information
East Asian mathematical journal / v.28, no.5, 2012 , pp. 569-578 More about this Journal
Abstract
In this paper, the necessary and sufficient conditions for the strong convergence of a modified Mann iteration process to a fixed point of an asymptotically demicontractive mapping in real Banach spaces are considered. Presented results improve and extend the results of Igbokwe [3], Liu [4], Moore and Nnoli [6] and Osilike [7].
Keywords
Modified Mann iteration method; uniformly L-Lipschitzian mapping; asymptotically demicontractive mapping; asymptotically pseudocontractive mapping;
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1 S. S. Chang, On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces, J. Math. Anal. Appl. 216 (1997), 94-111.   DOI   ScienceOn
2 C. E. Chidume and S. Maruster, Iterative methods for the computation of fixed points of demicontractive mappings, J. Comput. Appl. Math. 234 (3) (2010), 861-882.   DOI   ScienceOn
3 D. I. Igbokwe, Approximation of fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces, J. Ineq. Pure Appl. Math. 3 (1) (2002), Article 3.
4 Q. H. Liu, Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings, Nonlinear Analysis 26 (11) (1996), 1835-1842.   DOI   ScienceOn
5 W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.   DOI   ScienceOn
6 C. Moore and B. V. C. Nnoli, Iterative sequence for asymptotically demicontractive maps in Banach spaces, J. Math. Anal. Appl. 302 (2) (2005), 557-562.   DOI   ScienceOn
7 M. O. Osilike, Iterative approximations of fixed points of asymptotically demicontractive mappings, Indian J. Pure Appl. Math. 29 (12) (1998), 1291-1300.
8 J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991), 407-413.   DOI
9 K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301-308.   DOI   ScienceOn