A Nash type solution for hemivariational inequality systems

TL;DR

This paper establishes the existence of solutions for hemivariational inequality systems using fixed point theorems, extending to infinite dimensions and applying to Nash generalized derivative points.

Contribution

It introduces a new existence theorem for hemivariational inequalities systems and extends Nash generalized derivative points to infinite-dimensional spaces.

Findings

Existence of solutions proved using Ky Fan and Tarafdar theorems.

Extension of Nash generalized derivative points to infinite-dimensional spaces.

Application to general hemivariational inequalities systems.

Abstract

In this paper we prove an existence result for a general class of hemivariational inequalities systems using the Ky Fan version of KKM theorem (1984) or the Tarafdar fixed point theorem (1987). As application we give an infinite dimensional version for existence result of Nash generalized derivative points introduced recently by Krist\'{a}ly (2010) and also we give an application to a general hemivariational inequalities system.