Variational inequalities and fixed point problems : a survey
Renu Chugh, Rekha Rani · International Journal of Applied Mathematical Research · 2014
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.