Modified Proximal point algorithms for finding a zero point of maximal monotone operators, generalized mixed equilibrium problems and variational inequalities

In this article, we prove strong and weak convergence theorems of modified proximal point algorithms for finding a common element of the zero point of maximal monotone operators, the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems and the fixed point set of relatively nonexpansive mappings in a Banach space under difference conditions. Our results modify and improve previous result of Li and Song.