Abstract
Abstract We show that given a convex subset K of a topological vector space X and a multivalued map T : K ⇉ X ∗ , if there exists a nonempty subset S of X ∗ with the surjective property on K and T + w is quasimonotone for each w ∈ S , then T is monotone. Our result is a new version of the result obtained by N. Hadjisavvas (Appl. Math. Lett. 19:913-915, 2006).
Highlights
Introduction and some definitionsThroughout the paper, X and X* denote a real topological vector space and the dual space of X, respectively
Suppose K ⊆ X is a nonempty subset of X and T : K ⇒ X* is a multivalued map from K to X*
It is clear that a monotone map is pseudomonotone, while a pseudomonotone map is quasimonotone
Summary
Introduction and some definitionsThroughout the paper, X and X* denote a real topological vector space and the dual space of X, respectively. Suppose K ⊆ X is a nonempty subset of X and T : K ⇒ X* is a multivalued map from K to X*. In the case of a single-valued linear map T defined on the whole space Rn, it is known that if T + w is quasimonotone, T is monotone [ ].
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