Existence Results for Mixed Equilibrium Problems Involving Set-Valued Operators with Applications to Quasi-Hemivariational Inequalities

Bijaya Kumar Sahu (), Ouayl Chadli (), Ram N. Mohapatra () and Sabyasachi Pani ()
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Bijaya Kumar Sahu: Indian Institute of Technology Bhubaneswar
Ouayl Chadli: Ibn Zohr University
Ram N. Mohapatra: University of Central Florida
Sabyasachi Pani: Indian Institute of Technology Bhubaneswar

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 3, No 5, 810-823

Abstract: Abstract In this paper, we study the existence of solutions for mixed equilibrium problems associated with a set-valued operator in the general setting of vector spaces in duality, and in particular in Banach spaces. We use a Galerkin-type method and the notion of pseudomonotonicity in the sense of Brézis for bifunctions. As application, we study the existence of solutions for quasi-hemivariational inequalities governed by a set-valued mapping and perturbed with a nonlinear term. Our main results can be applied to differential inclusions, evolution equations and evolution hemivariational inequalities.

Keywords: Set-valued variational inequalities; Equilibrium problems; Set-valued mapping; Pseudomonotonicity; Hemivariational inequalities; 47H04; 47J20; 49J40; 47H10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-019-01629-1

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