A New Iterative Algorithm for Multivalued Nonexpansive Mappping and Equlibruim Problems with Applications

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Sow Thierno Mohadamane Mansour

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Journal Paper

Paper Information

Journal: SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS (SCMA) Year:2020 | Volume:17 | Issue:2 Page(s): 1-22

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Title

A New Iterative Algorithm for Multivalued Nonexpansive Mappping and Equlibruim Problems with Applications

Author(s)

Sow Thierno Mohadamane Mansour | Issue Writer Certificate

Keywords

Multivalued mappings

Equilibrium problems

Iterative methods

Applications

Abstract

In this paper, we introduce two iterative schemes by a modified Krasnoselskii-Mann algorithm for finding a common element of the set of solutions of Equilibrium problems and the set of fixed points of multivalued nonexpansive mappings in Hilbert space. We prove that the sequence generated by the proposed method converges strongly to a common element of the set of solutions of equilibruim problems and the set of fixed points of multivalued nonexpansive mappings which is also the minimum-norm element of the above two sets. Finally, some Applications of our results to optimization problems with constraint and the split feasibility problem are given. No compactness assumption is made. The methods in the paper are novel and different from those in early and recent literature.

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