The Tikhonov regularization for equilibrium problems and applications to quasi-hemivariational inequalities

The Ekeland variational principle for equilibrium problems revisited and applications

“…In [16,10], some equilibrium problems' techniques have been employed to solve the quasi-hemivariational inequality (QHVI). There are two bifunctions approach considered in this study.…”

“…In the sequel, we make use of some techniques of semicontinuity of functions on a subset introduced recently in [18,16,10] to obtain new results concerning the existence of solutions of nonconvex equilibrium problems.…”

“…In this paper, the set A is not assumed to be necessarily convex which leads to an interesting case of equilibrium problems called sometimes nonconvex equilibrium problems, see [10] and the references therein.…”

“…In this direction, we consider quasi-hemivariational inequalities introduced in [13]. Quasi-hemivariational inequalities are generalization of multivalued variational inequalities and several connections with equilibrium problems are obtained, see also [14][15][16]10] for recent and old investigations on the subject. Our approach is based on a result of [15] stating that a point is a solution of a quasi-hemivariational inequality if and only if it is a fixed point of a suitable multivalued mapping.…”

“…The converse holds under additional conditions on the values of the set-valued mapping A, see[10, Theorem 4.1].…”