Abstract
This paper is focused on the modified Ishikawa iterative scheme by admitting that the parameterizing sequences might be vectors of distinct components. It is also assumed that the auxiliary self-mapping which supports the iterative scheme is asymptotically demicontractive.
Highlights
The study of iterative methods such as Krasnoselsky, Mann, and Ishikawa iterations as well as a large variety of extensions and their convergence properties have received special attention in the last decades
Some definitions and auxiliary results are given to be invoked
Let S be a nonempty subset of a normed linear space E and let T : S → S be a mapping
Summary
The study of iterative methods such as Krasnoselsky, Mann, and Ishikawa iterations as well as a large variety of extensions and their convergence properties have received special attention in the last decades. It is found in [12] that continuous monotone and generalized quasi-nonexpansive self-mappings on nonempty compact and convex subsets of Hilbert spaces converge strongly to one of their fixed points under Ishikawa’s iterative scheme under certain standard conditions of its parameterizing sequences.
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