New Convergence Theorems for Maximal Monotone Operators in Banach Spaces

Convergence Theorems for Generalized Projections and Maximal Monotone Operators in Banach Spaces

Strong Convergence Theorems of Multivalued Nonexpansive Mappings and Maximal Monotone Operators in Banach Spaces

In this paper, we prove a strong convergence theorem for fixed points of sequence for multivalued nonexpansive mappings and a zero of maximal monotone operator in Banach spaces by using the hybrid projection method. Our results modify and improve the recent results in the literatures.

Existence and Perturbation Theorems for Nonlinear Maximal Monotone Operators in Banach Spaces by Felix E. Browder

Such a set G is said to be maximal monotone if it is maximal among monotone sets in the sense of set inclusion, and a mapping T is said to be maximal monotone if its graph G(T) is a maximal monotone set. For reflexive Banach spaces X and mappings T with D(T)~X, the basic result obtained independently by Browder [2] and Minty [20] states that if T is a monotone operator from D(T)=X to X* which i...

Convergence Theorems of Approximate Proximal Point Algorithm for Zeroes of Maximal Monotone Operators in Hilbert Spaces

In this paper, we introduce two kinds of iterative algorithms for finding zeroes of maximal monotone operators, and establish strong and weak convergence theorems of the modified proximal point algorithms. By virtue of the established theorems, we consider the problem of finding a minimizer of a convex function. Mathematics Subject Classification: Primary 47H17; Secondary 47H05, 47H10

Strong convergence theorems for quasi-nonexpansive mappings and maximal monotone operators in Hilbert spaces

We present the strong convergence theorem for the iterative scheme for finding a common element of the fixed-point set of a quasi-nonexpansive mapping and the zero set of the sums of maximal monotone operators in Hilbert spaces. Our results extend and improve the recent results of Takahashi et al. (J. Optim. Theory Appl. 147:27-41, 2010) and Takahashi and Takahashi (Nonlinear Anal. 69:1025-1033...