A mixed monotone variational inequality MMVI problem in a Hilbert space H is formulated to find a point u∗ ∈ H such that 〈Tu∗, v − u∗〉 φ v − φ u∗ ≥ 0 for all v ∈ H, where T is a monotone operator and φ is a proper, convex, and lower semicontinuous function onH. Iterative algorithms are usually applied to find a solution of an MMVI problem. We show that the iterative algorithm introduced in the ...

We investigate the Nash-Cournot oligopolistic market equilibrium model with concave cost function. We show that in this case the model can be formulated as a mixed variational inequality on its convex, compact strategy set, which, in general, may fail to exist an equilibrium point. We give conditions under which the model has an equilibrium point. We then propose an algorithm for finding an equ...

We study maximal monotone inclusions from the perspective of (convex) gap functions. We propose a very natural gap function and will demonstrate how this function arises from the Fitzpatrick function — a convex function used effectively to represent maximal monotone operators. • This approach allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. – We...

We introduce new iterative algorithms by hybrid method for finding a common element of the set of solutions of fixed points of infinite family of nonexpansive mappings, the set of common solutions of generalized mixed equilibrium problems, and the set of common solutions of the variational inequality with inverse-strongly monotone mappings in a real Hilbert space. We prove the strong convergenc...

We introduce a new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of k-strictly pseudocontractive mappings and the set of common solutions to a system of generalized mixed equilibrium problems and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to...

We introduce a new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings, the set of common solutions to a system of generalized mixed equilibrium problems, and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to a common element ...

We introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a β-inversestrongly monotone mapping, and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Cesàro mean approximation method. We prove that the sequenc...

Correspondence: [email protected] Institute of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, P. R China Abstract In this article, we prove the existence of solutions for the general variational inequality j(x, y) ≥ f(x) f(y) and Minty type theorem by using the generalized KKM theorem in topological spaces without linear structure. Some properties of solutions set for t...

In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a demicontinuous nearly nonexpansive mapping. We prove that the proposed method converges strongly to a common solution of above problems under the suitable conditions. It is also noted that the main ...

We introduce a new iterative method for finding a common element of the set of fixed points of a strictly pseudocontractive mapping, the set of solutions of a generalized mixed equilibrium problem, and the set of solutions of a variational inequality problem for an inverse-stronglymonotone mapping in Hilbert spaces and then show that the sequence generated by the proposed iterative scheme conve...