Convergence theorems for monotone vector field inclusions and minimization problems in Hadamard spaces

Monotone and Pseudo-monotone Equilibrium Problems in Hadamard Spaces

As a continuation of previous work of the first author with S. Ranjbar [26] on a special form of variational inequalities in Hadamard spaces, in this paper we study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with pseudomon...

Convergence Theorems for -Nonexpansive Mappings in CAT(0) Spaces

In this paper we derive convergence theorems for an -nonexpansive mappingof a nonempty closed and convex subset of a complete CAT(0) space for SP-iterative process and Thianwan's iterative process.

Global Convergence of a Closed-Loop Regularized Newton Method for Solving Monotone Inclusions in Hilbert Spaces

We analyze the global convergence properties of some variants of regularized continuous Newton methods for convex optimization and monotone inclusions in Hilbert spaces. The regularization term is of LevenbergMarquardt type and acts in an open-loop or closed-loop form. In the open-loop case the regularization term may be of bounded variation.

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

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...