A Study On Variational Inequalities

Abstract

The main objective of the thesis is to study and develop iterative algorithms for solving variational inequality problems using fixed point equivalence formulation of problem. New iterative algorithms are introduced to establish the weak and strong convergence theorems of common solution of variational inequality problem and fixed point of nonlinear mappings. We have proved strong convergence theorem for common solution of fixed point of asymptotically pseudocontractive mapping and certain variational inequality problem. A viscosity implicit rule and a viscosity approximation method is introduced to prove common fixed point theorem of asymptotically pseudocontractive mapping and firmly nonexpansive mapping which solves a certain variational inequality problem. To support and applicability of the theorems proved, we have presented some numerical examples also. As an application we have also introduced X-ray tomographic reconstruction using H(., .)and#8722;and#968; and#8722;and#951;-accretive mapping. A Hybrid steepest descent method and a proximal point algorithm is developed for solving strong convergence of variational inequality problem. newline newline