Approximate Fixed Point Theorems for the Class of Almost "Equation missing" -"Equation missing" Mappings in Abstract Convex Uniform Spaces

Abstract

We use a concept of abstract convexity to define the almost "Equation missing"-"Equation missing" property, al-"Equation missing"-"Equation missing" family, and almost "Equation missing"-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost "Equation missing"-spaces. Our results extend some results of other authors.

A system of nonlinear set valued variational inclusions

“…In recent years, the classical variational inequality and complementarity problems have been extended and generalized to study a large variety of problems arising in economics, control problems, contact problems, mechanics, transportation, equilibrium problems, optimization theory, nonlinear programming, transportation equilibrium and engineering sciences, see (Aubin 1982; Baiocchi and Capelo 1984; Chang 1984; Giannessi and Maugeri 1995). Hassouni and Moudafi 2001 introduced and studied a class of mixed type variational inequalities with single valued mappings which was called variational inclusions.…”