Approximating Common Solutions Of Variational Inequality Equilibrium And Fixed Point Problems

Many of the most important problems arising in nonlinear analysisrnreduce to solving a given equation, which in turn may be reduced tornfinding the fixed points of a certain mapping or solutions of varia-rntional inequality and equilibrium problems. Because of the relationrnbetween the fixed point problem, variational inequality and equilib-rnrium problems, finding common solutions of these problems is anrnimportant field of research.rnIn this thesis, we introduce and study an iterative algorithm whichrnconverges strongly to a common element of the set of xed points ofrna more general class of Lipschitz hemicontractive-type multi-valuedrnmappings and the set of solutions of variational inequality problem inrnreal Hilbert spaces. In addition, we have obtained strong convergencerntheorems of an iterative process for finding a common solution of thernfixed point problem for Lipschitz hemicontractive-type multi-valuedrnmapping and the generalized equilibrium problem in the frameworkrnof real Hilbert spaces. We also extend this result to a finite familyrnof generalized equilibrium problems. Furthermore, a viscosity-typernapproximation method is introduced for approximating a commonrnelement of the set of fixed points of a nonexpansive multi-valuedrnmapping, the sets of solutions of a split equilibrium and a variationalrninequality problems.

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