Existence and iterative algorithm of solutions for a new system of generalized set-valued mixed equilibrium-like problems in Banach spaces

摘要

A new system of generalized set-valued mixed equilibrium-like problems (in short, S-GMELP) in Banach spaces is discussed. In order to obtain the existence of solutions of S-GMELP, a system of related auxiliary problems (in short, S-AP) is established. On the basis of the existence and uniqueness of solutions of the S-AP, an iterative algorithm for the S-GMELP is constructed. It is proved that the iterative sequence converges some solution of S-GMELP. Finally, an example is given to well exemplify our main result.