<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

Data publikacji: 26 gru 2019

Zakres stron: 559 - 574

Otrzymano: 14 wrz 2019

Przyjęty: 28 wrz 2019

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

Słowa kluczowe
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

Data publikacji: 26 gru 2019

Zakres stron: 559 - 574

Otrzymano: 14 wrz 2019

Przyjęty: 28 wrz 2019

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

Słowa kluczoweDemicontractive 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.

Słowa kluczowe
Demicontractive mappings, Quasi-nonexpansive mappings, Common fixed points, Accretive operators