Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings

Osilike, Micah Okwuchukwu; Onah, Anthony Chibuike

doi:10.1515/awutm-2015-0008

Abstract

A new class of α-hemicontractive maps T for which the strong convergence of the Ishikawa iteration algorithm to a fixed point of T is assured is introduced and studied. The study is a continuation of a recent study of a new class of α-demicontractive mappings T by L. Mărușter and Ș. Mărușter, Mathematical and Computer Modeling 54 (2011) 2486-2492 in which they proved strong convergence of the Mann iteration scheme to a fixed point of T. Our class of α-hemicontractive maps is more general than the class of α-demicontractive maps. No compactness assumption is imposed on the operator or it’s domain, and no additional requirement is imposed on the set of fixed points.

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Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings

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