Strong Convergence of New Algorithm for Monotone Operator in Banach Spaces. (10th September 2019) - Tang, Yan
Abstract: Let E be a uniformly convex and uniformly smooth real Banach space with dual E * . 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 x * ∈ A − 1 ( 0 ) 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.