This paper studies the proximal point algorithm for class of generalized variational inequalities. By using upper semicontinuity result establishing weakly univalent operators, we show that iterative sequence generated by is bounded, approaches to solution set initial problem, and each its accumulation points a provided bounded. We also give an example necessity boundedness.

‎The proximal point algorithm‎, ‎which is a well-known tool for finding‎ ‎minima of convex functions‎, ‎is generalized from the classical‎ ‎Hilbert space framework into a nonlinear setting‎, ‎namely‎, ‎geodesic‎ ‎metric spaces of nonpositive curvature‎. ‎In this paper we propose an‎  ‎iterative algorithm for finding the common element of the‎ ‎minimizers of a finite family of convex functions a...

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...

This paper presents a class of proximal point algorithms (PPA) with nonlinear proximal terms. Proximal minimization algorithm using Bregman distance for convex minimization is extended for solving monotonic variational inequalities. Under suitable conditions, the convergence and O(1/N) computing complexity/convergence rate of the proposed algorithm is obtained. Further more, connections to some...