Generalized monotone mixed equilibrium problems in FC-spaces: Existence and approximation

Abstract

In this paper, we study a class of mixed equilibrium problems under the extended generalized α–η monotonicity in finitely continuous topological spaces. Existence of solutions to the problems is established by relaxing the convexity structure and the linearity condition by using the relatively Knaster-Kuratowski-Mazurkiewicz principle. We also propose an iterative scheme based on auxiliary principle techniques. The results obtained in this paper improve and generalize some recent results in the framework of FC spaces under weaker conditions. They are useful to solve problems, where the domain and range of the underlying mappings lack the convexity structure.