In this paper, we propose a new generalized mixed equilibrium problem which includes many existing monotone equilibrium problems and their derivatives. Using the KKM technique, we establish the existence of solutions of the proposed problem under suitable conditions. Furthermore, we introduce an iterative algorithm for solving the problem and prove its strong convergence in Banach spaces. Several numerical examples illustrate the efficiency of the algorithm.
|Number of pages||21|
|Journal||Journal of Nonlinear and Convex Analysis|
|Publication status||Published - 2020|
- Existence result
- KKM technique
- New generalized mixed equilibrium problem
- Reflexive Banach space