A Tikhonov-type regularization for Brézis pseudomonotone equilibrium problems in Banach spaces
Journal of Applied and Numerical Optimization · 2021
In this paper, we study the existence of solutions for nonmonotone equilibrium problems by a Tikhonov weak regularization scheme and a Galerkin-type method.In our approach, we use the notion of the pseudomonotonicity in the sense of Brézis for bifunctions initially introduced by Gwinner, and we do not assume that the considered bifunction is lower semicontinuous with respect to the second argument.We use suitable weakened coercivity conditions to obtain the convergence of generalized versions of the Tikhonov regularization procedure for nonmonotone equilibrium problems.Our results, which can be applied to rather class of nonlinear and nonmonotone problems associated to pseudomonotone operators in the sense of Brézis, are new and extend some previous results in literature.