Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2017; 54(3): 1031-1047

Online first article January 4, 2017      Printed May 1, 2017

https://doi.org/10.4134/JKMS.j160352

Copyright © The Korean Mathematical Society.

Strong convergence of general iterative algorithms for nonexpansive mappings in Banach spaces

Jong Soo Jung

Dong-A University

Abstract

In this paper, we introduce two general iterative algorithms (one implicit algorithm and other explicit algorithm) for nonexpansive mappings in a reflexive Banach space with a uniformly G\^ateaux differentiable norm. Strong convergence theorems for the sequences generated by the proposed algorithms are established.

Keywords: nonexpansive mapping, general iterative algorithms, strong positive linear operator, strongly pseudocontractive mapping, fixed points, uniformly G\^ateaux differentiable norm

MSC numbers: 47H10, 47H09