Strong Convergence of New Algorithm for Monotone Operator in Banach Spaces
Yan Li Tang · Numerical Functional Analysis and Optimization · 2019
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.