In this paper we introduce some new conditions of the solu- tions existence for variational-like inequalities with relaxed &eta-&alpha pseu- domonotone mappings in Banach spaces. The advantage of these new conditions is that they are easier to be veried than those that appear in some of the previous corresponding articles.

We deal with mappings defined between Riemannian manifolds that belong to trace spaces of Sobolev functions. Such mappings are equipped with a natural energy, equivalent to the fractional norm. We study the class of Cartesian currents that arise as weak limits of sequences of mappings with equibounded energies. Under suitable topological assumptions on the domain and target manifolds, we prove ...

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Further...

In this paper, we introduce two concepts of weakly relaxed {ηγ − αγ}γ∈Γ pseudomonotone and demipseudomonotone mappings in Banach spaces. Then we obtain some results of the solutions existence for a system of vector variational-like inequalities with weakly relaxed {ηγ − αγ}γ∈Γ pseudomonotone and demipseudomonotone mappings in reflexive Banach spaces. Finally we show that our results improve and...