WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Existence and Iterative Algorithm of Solutions for a New System of Generalized Set-Valued Mixed Equilibrium-Like Problems in Banach Spaces
Authors: ,
Abstract: A new system of generalized set-valued mixed equilibrium-like problems (in short, S-GMELP) in Ba- nach 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.