A class of nonlinear variational inequalities involving pseudomonotone operators.
A converse to the Lions-Stampacchia theorem
In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.
A converse to the Lions-Stampacchia Theorem
In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.
A general duality principle for the sum of two operators.
A general iterative approach to variational inequality problems and optimization problems.
A general projection method for a system of relaxed cocoercive variational inequalities in Hilbert spaces.
A general vector-valued variational inequality and its fuzzy extension.
A generalized hybrid steepest-descent method for variational inequalities in Banach spaces.
A generalized iterative algorithm for generalized successively pseudocontractions.
A Gregus type common fixed point theorem in normed spaces with applications.
A hybrid iterative scheme for a maximal monotone operator and two countable families of relatively quasi-nonexpansive mappings for generalized mixed equilibrium and variational inequality problems.
A hybrid method for monotone variational inequalities involving pseudocontractions.
A hybrid-extragradient scheme for system of equilibrium problems, nonexpansive mappings, and monotone mappings.
-monotonicity and applications to nonlinear variational inclusion problems.
A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings.
A new hybrid iterative algorithm for fixed-point problems, variational inequality problems, and mixed equilibrium problems.
A new projection algorithm for generalized variational inequality.
A new system of nonlinear fuzzy variational inclusions involving -accretive mappings in uniformly smooth Banach spaces.
A note on Minty type vector variational inequalities
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space are introduced....
A note on Minty type vector variational inequalities
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are introduced. Under...