Strong Convergence of New Algorithm for Monotone Operator in Banach Spaces

Abstract

Let E be a uniformly convex and uniformly smooth real Banach space with dual The convergence of a new iterative algorithm for approximating zero points of monotone (not strongly monotone) and bounded mapping is established and analyzed. The algorithm is proved to converge strongly to which is not involving the resolvent operator. Moreover, applications to solutions of variational inequality problems, convex minimization problems and a cluster of semi-pseudo mappings are included. Numerical results are reported to illustrate the behavior of the algorithm with different sequences of stepsizes and also to compare it with other algorithms.