In this paper, we introduce viscosity approximation methods based on generalized contractionmappings for finding a set of common fixed points of a countable family of strict pseudo-contractionmappings, the commonelement of the set solutions of a general system of variational inequalities with Lipschitzian and relaxed cocoercive mappings and the set of solutions of a generalizedmixed equilibrium...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

‎In a real Hilbert space‎, ‎an iterative scheme is considered to‎ ‎obtain strong convergence which is an essential tool to find a‎ ‎common fixed point for a countable family of nonexpansive mappings‎ ‎and the solution of a variational inequality problem governed by a‎ ‎monotone mapping‎. ‎In this paper‎, ‎we give a procedure which results‎ ‎in developing Shehu's result to solve equilibrium prob...

We show that the variational inequality $VI(C,A)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-Lipschitzian mapping $A: Cto H$ with $r>gamma mu^2$, where$C$ is a nonempty closed convex subset of a Hilbert space $H$. Fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...

§0 Introduction §1 First and Second Variational Formulas for Area §2 Bishop Comparison Theorem §3 Bochner-Weitzenböck Formulas §4 Laplacian Comparison Theorem §5 Poincaré Inequality and the First Eigenvalue §6 Gradient Estimate and Harnack Inequality §7 Mean Value Inequality §8 Reilly’s Formula and Applications §9 Isoperimetric Inequalities and Sobolev Inequalities §10 Lower Bounds of Isoperime...

In this paper, we use the auxiliary principle technique to study the existence of a solution of the extended general variational inequalities, which were introduced and studied by the author. Several special cases are also discussed.