<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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. </p></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.

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

Department of Mathematics, University of Nigeria, Nsukka, Nigeria

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

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

Published Online: Dec 12, 2015

Page range: 151 - 161

Received: Feb 23, 2015

Accepted: Mar 17, 2015

DOI: https://doi.org/10.1515/awutm-2015-0008

Keywords
α-demicontractive maps, α-hemicontractive maps, fixed points, Ishikawa iteration, strong convergence

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Dec 12, 2015

Page range: 151 - 161

Received: Feb 23, 2015

Accepted: Mar 17, 2015

DOI: https://doi.org/10.1515/awutm-2015-0008

Keywordsα-demicontractive maps, α-hemicontractive maps, fixed points, Ishikawa iteration, strong convergence

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
α-demicontractive maps, α-hemicontractive maps, fixed points, Ishikawa iteration, strong convergence