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

<p>In this paper, we suggest and analyze a new iterative method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of fixed points of a demicontractive mapping which is the unique solution of some variational inequality problems involving accretive operators in a Banach space. We prove the strong convergence of the proposed iterative scheme without imposing any compactness condition on the mapping or the space. Finally, applications of our theorems to some constrained convex minimization problems are given.</p>
</abstract>

In this paper, we suggest and analyze a new iterative method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of fixed points of a demicontractive mapping which is the unique solution of some variational inequality problems involving accretive operators in a Banach space. We prove the strong convergence of the proposed iterative scheme without imposing any compactness condition on the mapping or the space. Finally, applications of our theorems to some constrained convex minimization problems are given.

New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in Banach spaces

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 Public License.

In this paper, we suggest and analyze a new iterative method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the...

New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in Banach spaces

Published Online: Dec 26, 2019

Page range: 559 - 574

Received: Sep 14, 2019

Accepted: Sep 28, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00053

Keywords
Demicontractive mappings, Quasi-nonexpansive mappings, Common fixed points, Accretive operators

© 2019 T.M.M. Sow, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in Banach spaces

Published Online: Dec 26, 2019

Page range: 559 - 574

Received: Sep 14, 2019

Accepted: Sep 28, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00053

KeywordsDemicontractive mappings, Quasi-nonexpansive mappings, Common fixed points, Accretive operators

© 2019 T.M.M. Sow, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Keywords
Demicontractive mappings, Quasi-nonexpansive mappings, Common fixed points, Accretive operators