Applications of Variational Inequalities to Nonlinear Analysis

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Abstract

In this paper, we consider some applications of variational inequalities to nonlinear analysis. These applications include solutions of nonlinear equations, fixed point problems and eigenvalue problems. In particular, we show that any hemicontinuous and dissipative operator from a nonempty closed convex subset of a Hilbert space into itself has a unique fixed point. An iterative scheme for searching for fixed points of special types of operators is proposed.

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