# Variational inequalities and fixed point problems : a survey

## DOI:

https://doi.org/10.14419/ijamr.v3i3.2987## Published:

2014-08-12## Abstract

The variational inequality problem provides a broad unifying setting for the study of optimization, equilibrium and related problems and serves as a useful computational framework for the solution of a host of problems in very diverse applications. Variational inequalities have been a classical subject in mathematical physics, particularly in the calculus of variations associated with the minimization of infinite-dimensional functionals. This paper presents a survey of main results related to variational inequalities and fixed point problems defined on real Hilbert spaces and Banach spaces.

**Keywords**: Fixed Point Problem, Inverse-Strongly-Monotone Mappings, Monotone Mappings, Projection Mappings, Variational Inequality Problem.

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