Necessary and sufficient conditions for convergence of Ishikawa iterative schemes with errors to $\phi$-hemicontractive mappings
Commun. Korean Math. Soc. 2003 Vol. 18, No. 2, 251-261
Printed June 1, 2003
Zeqing Liu, Jong Kyu Kim, Shin Min Kang
Liaoning Normal University, Kyungnam University, Gyeongsang National University
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
MSC numbers : 47H05, 47H06, 47H10, 47H14
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