On pseudomonotone set-valued mappings

On Pseudomonotone Set-Valued Mappings in Topological Vector Spaces

“…The third generalization, which they called C-pseudomonotonicity, is a weaker notion and common generalization of the algebraic and topological pseudomonotonicity for set-valued maps. This paper is inspired and [2] On pseudomonotone set-valued mappings in topological vector spaces 259 motivated by [7]. In this paper we generalize the main results of [7] to the topological vector spaces.…”

“…This paper is inspired and [2] On pseudomonotone set-valued mappings in topological vector spaces 259 motivated by [7]. In this paper we generalize the main results of [7] to the topological vector spaces.…”

“…DEFINITION 2.1 (Inoan and Kolumban [7]). The mapping T is called A-pseudomonotone if, for every x, x ∈ X ,…”

“…The following definition generalizes the notion of topological pseudomonotonicity introduced by Brezis. [7]). The mapping T is called B-pseudomonotone if, for every x ∈ X and for every net {x i } i∈I in X with x i → x, f i ∈ T (x i ), and lim inf i x − x i , f i ≥ 0, implies that for every y ∈ X there exists f (y) ∈ T (x) such that lim sup…”

“…These two pseudomonotonicity concepts are different (see [7]). Inoan and Kolumban [7] studied three types of pseudomonotone set-valued mappings in a topological vector spaces setting. Two of them are generalizations of the classical notions mentioned above.…”