Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2002; 39(3): 455-469

Printed September 1, 2002

Copyright © The Korean Mathematical Society.

Convergence theorems and stability problems of the modified Ishikawa iterative sequences for strictly successively hemicontractive mappings

Zeqing Liu, Jong Kyu Kim, and Ki Hong Kim

Liaoning Normal University, Kyungnam University, Kyungnam University

Abstract

The purpose of this paper is to introduce the concept of a class of strictly successively hemicontractive mappings and construct certain stable and almost stable iteration procedures for the iterative approximation of fixed points for asymptotically nonexpansive and strictly successively hemicontractive mappings in Banach spaces.

Keywords: asymptotically nonexpansive mapping, modified Ishikawa iterative sequence with errors, stability, almost stability, strictly successively hemicontractive mapping

MSC numbers: 47H06, 47H09, 47H10