Strong convergence theorems for maximal monotone operators in Banach spaces

Abstract

Listen

Translate article

Let E be a uniformly convex and uniformly smooth Banach space with the dual E* and let T : E → 2 E* be a maximal monotone operator. By using the technique of resolvent operators and by using modified Ishikawa iteration and modified Halpern iteration for relatively non-expansive mappings, we suggest and analyse two iterative algorithms for finding an element x ∈ E such that 0 ∈ T(x). Strong convergence theorems for such iterative algorithms are proved. The ideas of these algorithms are applied to solve the problem of finding a minimizer of a convex function on E.