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

In this paper, we deal with the Tikhonov regularization method for pseudo-monotone equilibrium problems. Under mild conditions of semicontinuity and convexity, we show that strictly pseudo-monotone bifunctions can be also used as regularization bifunctions as well as strongly monotone bifunctions. We extend Berge’s maximum theorem and establish the relationship between quasi-hemivariational inequalities and equilibrium problems. Applications of the Tikhonov regularization method to quasi-hemivariational inequalities are also given.

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