This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-φ-nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.

Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.

This paper presents some new fixed point theorems./i~r fuzzy mappings. The results given in this paper improve and extend some recent results of [l, 4. 5].

The purpose of this paper is to study the existence and iterative approxhnation of minimax quasi-solutions for a class of initial vahte problems of.first order hnpulsive differential systems by using monotone iterative methods.

Fixed point theorems for fuzzy mappings are of fundamental importance in fuzzy mathematical theory and application investigation.This paper pressents some new fixed point theorems for fuzzy mapping, whose results generalize and improve the results of [3] and give a partial answer to the unsolved problem suggested in [i].