COMMON SOLUTIONS TO SOME SYSTEMS OF VECTOR EQUILIBRIUM PROBLEMS AND COMMON FIXED POINT PROBLEMS IN BANACH SPACE

Abstract

In this paper, we study some properties of set of solutions of a new generalized mixed vector equilibrium problem in Banach space. Further, we introduce an iterative method based on hybrid method and convex approximation method for finding a common element to the set of solutions of a system of unrelated generalized mixed vector equilibrium problems and the set of solutions of common fixed point problems for the two families of generalized asymptotically quasi $\phi$-nonexpansive mappings in Banach space. Furthermore, we obtain a strong convergence theorem for the sequences generated by the proposed iterative scheme. Finally, we derive some consequences from our main result. The results presented in this paper extended and unify many of the previously known results in this area.