By considering the new forms of notions lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity considered scalar multiple integral functional, in this paper we study well-posedness a class variational problems with inequality constraints. More specifically, by defining set approximating solutions for under study, establish several results on well-posedness.

Generalised convexity is revisited from a geometrical point of view. A substitute to the subdifferential is proposed. Then generalised monotonicity is considered. A representation of generalised monotone maps allows to obtain a symmetry between maps and their inverses. Finally, maximality of generalised monotone maps is analysed.

By using the monotonicity, hemicontinuity, and pseudomonotonicity of considered integral functionals, we studied well-posedness some variational inequality problems governed by partial derivatives second-order. To this aim, introduce approximating solution set concept sequences for controlled problem. Further, aforementioned new mathematical tools, established theorems on well-posedness. Moreov...

This paper deals with the convergence of the algorithm built on the auxiliary problem principle for solving a class of pseudomonotone type mixed variational-like inequalities. The convergence criteria of this method are presented under a joint pseudo-Dunn property or a joint strong pseudomonotonicity assumption on the operators involved in the mixed variational-like inequality problem. Moreover...

Some iterative methods for solving equilibrium problems are suggested and analyzed by using the technique of the auxiliary principle. We have shown that the convergence of the proposed methods either requires only pseudomonotonicity, which is a weaker condition than monotonicity or partially relaxed strongly monotonicity. Our results represent an improvement and refinement of previously known r...

In this paper, we consider and study a new class of hemivariational inequalities, which is called trifunction hemivariational inequality. We suggest and analyze a class of iterative methods for solving trifunction hemivariational inequalities using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pse...

We propose a strongly convergent algorithm for finding a common point in the solution set of a class of pseudomonotone equilibrium problems and the set of fixed points of nonexpansive mappings in a real Hilbert space. The proposed algorithm uses only one projection and does not require any Lipschitz condition for the bifunctions. AMS 2010 Mathematics subject classification: 65 K10, 65 K15, 90 C...

This paper presents a predictor-corrector algorithm for solving the strongly nonlinear general noncovex variational inequality, which is a class of nonconvex variational inequalities involving three nonlinear operators. We establish the equivalence between the strongly nonlinear general nonconvex variational inequalities and the fixed point problem, and show that the convergence of the predicto...

In this paper, we consider variational inequality problem over the product of sets which is equivalent to the problem of system of variational inequalities. These two problems are studied for single valued maps as well as for multivalued maps. New concept of pseudomonotonicity in the sense of Brézis is introduced to prove the existence of a solution of our problems. As an application of our res...