# NECESSARY AND SUFFICIENT CONDITIONS FOR CONVERGENCE OF ISHIKAWA ITERATIVE SCHEMES WITH ERRORS TO φ-HEMICONTRACTIVE MAPPINGS

Liu, Seqing;Kim, Jong-Kyu;Kang, Shin-Min

• Published : 2003.04.01
• 40 3

#### Abstract

The purpose of this paper is to establish the necessary and sufficient conditions which ensure the strong convergence of the Ishikawa iterative schemes with errors to the unique fixed point of a $\Phi$-hemicontractive mapping defined on a nonempty convex subset of a normed linear space. The results of this paper extend substantially most of the recent results.

#### Keywords

${\Phi}$-hemicontractive mapping;strongly pseudocontractive mapping;${\Phi}$-strongly pseudocontractive mapping;strictly hemicontractive mapping;Ishikawa iterative scheme with errors

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