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...

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...

By variational methods, we prove the inequality ∫

We introduce an iterative method for finding a common element of the set of solutions of equilibrium problems, the set of solutions of variational inequality problems, and the set of fixed points of finite many nonexpansive mappings. We prove strong convergence of the iterative sequence generated by the proposed iterative algorithm to the unique solution of a variational inequality, which is th...

We prove sufficient conditions for the monotonicity and the strong monotonicity of fixed point and normal maps associated with variational inequality problem over a general closed convex set. Sufficient conditions for the strong monotonicity of their perturbed versions are also shown. These results include some known ones in the literature as particular instances. Inspired by these results, we ...