NECESSARY AND SUFFICIENT CONDITIONS FOR CONVERGENCE OF ISHIKAWA ITERATIVE SCHEMES WITH ERRORS TO φ-HEMICONTRACTIVE MAPPINGS
S.J. Liu, Jong-Kyu Kim, Shin-Min Kang · Communications of the Korean Mathematical Society · 2003
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.