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

<p>We introduce a new iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive mapping in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive. Futhermore, we applied our main result for finding a common solution of convex minimization problem and fixed points problem. Essentially a new approach for finding solutions of equilibrium problems and fixed point problems whith set-valued operators is provided.</p>
</abstract>

We introduce a new iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive mapping in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive. Futhermore, we applied our main result for finding a common solution of convex minimization problem and fixed points problem. Essentially a new approach for finding solutions of equilibrium problems and fixed point problems whith set-valued operators is provided.

A new fixed point technique for equilibrium problem with a finite family of multivalued quasi-nonexpansive mappings

General Mathematics

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

We introduce a new iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set...

A new fixed point technique for equilibrium problem with a finite family of multivalued quasi-nonexpansive mappings

Published Online: Nov 24, 2023

Page range: 119 - 134

Received: Oct 18, 2019

Accepted: Nov 09, 2022

DOI: https://doi.org/10.2478/gm-2022-0009

Keywords
Set-valued operators, Equilibrium problem, Fixed point algorithm

© 2022 T.M.M. Sow, published by Sciendo

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

A new fixed point technique for equilibrium problem with a finite family of multivalued quasi-nonexpansive mappings

Published Online: Nov 24, 2023

Page range: 119 - 134

Received: Oct 18, 2019

Accepted: Nov 09, 2022

DOI: https://doi.org/10.2478/gm-2022-0009

KeywordsSet-valued operators, Equilibrium problem, Fixed point algorithm

© 2022 T.M.M. Sow, published by Sciendo

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

Keywords
Set-valued operators, Equilibrium problem, Fixed point algorithm