Approximating Common Solutions of Variational Inequality, Equilibrium and Fixed Point Problems
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Date
2017-04
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Addis Ababa University
Abstract
Many of the most important problems arising in nonlinear analysis
reduce to solving a given equation, which in turn may be reduced to
finding the fixed points of a certain mapping or solutions of varia-
tional inequality and equilibrium problems. Because of the relation
between the fixed point problem, variational inequality and equilib-
rium problems, finding common solutions of these problems is an
important field of research.
In this thesis, we introduce and study an iterative algorithm which
converges strongly to a common element of the set of xed points of
a more general class of Lipschitz hemicontractive-type multi-valued
mappings and the set of solutions of variational inequality problem in
real Hilbert spaces. In addition, we have obtained strong convergence
theorems of an iterative process for finding a common solution of the
fixed point problem for Lipschitz hemicontractive-type multi-valued
mapping and the generalized equilibrium problem in the framework
of real Hilbert spaces. We also extend this result to a finite family
of generalized equilibrium problems. Furthermore, a viscosity-type
approximation method is introduced for approximating a common
element of the set of fixed points of a nonexpansive multi-valued
mapping, the sets of solutions of a split equilibrium and a variational
inequality problems.
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Keywords
Approximating Common, Solutions of Variational