New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces

We introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotone mappings. Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibrium problem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the fixed point set of an asymptotically nonexpansive mapping. The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The main results extend various results existing in the current literature

Existence and continuity for the ε-approximation equilibrium problems in Hadamard spaces

Abstract In this paper, the existence of ε-approximate equilibrium points for a bifunction is proved under suitable conditions in the framework of a Hadamard space. We also give the sufficient conditions for the continuity of ε-approximate solution maps to equilibrium problems. Then we apply our results to constrained minimization problems and Nash-equilibrium problems

A New Iterative Scheme for Solving the Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces

We introduce the new iterative methods for finding a common solution set of monotone, Lipschitz-type continuous equilibrium problems and the set of fixed point of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Hilbert space. The main result extends various results existing in the current literature