Let C be a nonempty closed convex subset of a uniformly convex and 2-uniformly smooth Banach space E and let Π<Subscript> C </Subscript> be a sunny nonexpansive retraction from E onto C. Let the mappings <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${T, S: C \to E}$$</EquationSource> </InlineEquation> be γ <Subscript>1</Subscript>-strongly accretive, μ <Subscript>1</Subscript>-Lipschitz continuous and γ <Subscript>2</Subscript>-strongly accretive, μ...</subscript></subscript></subscript></subscript></equationsource></inlineequation></subscript>

A uniqueness theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Three examples are given to demonstrate the...

In this work, strong convergence theorems by the viscosity approximation method associated with Meir–Keeler contractions are established for solving fixed point problems of a nonexpansive semigroup, a system of equilibrium problems and variational inequality problems in a real Hilbert space....

In this paper, we introduce a new hybrid iterative scheme for finding a common element of the set of zeroes of a maximal monotone operator, the set of fixed points of a relatively quasi-nonexpansive mapping, the sets of solutions of an equilibrium problem and the variational inequality problem...

The concept of pseudomonotone vector field on Hadamard manifold is introduced. A variant of Korpelevich’s method for solving the variational inequality problem is extended from Euclidean spaces to constant curvature Hadamard manifolds. Under a pseudomonotone assumption on the underlying vector...

In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on well-known projection method and the hybrid (or outer approximation) method. However we do not use an...