Bilevel minimax theorems for non-continuous set-valued mappings

Minimax Theorems for Set-Valued Mappings under Cone-Convexities

and Applied Analysis 3 Lemma 2.4 see 9, Lemma 3.1 . Let X, Y, and Z be three topological spaces. Let Y be compact, F : X × Y ⇒ Z a set-valued mapping, and the set-valued mapping T : X ⇒ Z defined by T x ⋃ y∈Y F ( x, y ) , ∀x ∈ X. 2.2 a If F is upper semi-continuous on X × Y, then T is upper semi-continuous on X. b If F is lower semi-continuous onX, so is T. Lemma 2.5 see 9, Lemma 3.2 . Let Z be...

Fixed Point Theorems for Set-valued Mappings

Some Fixed Point Theorems for Nonlinear Set-Valued Contractive Mappings

Convergence Theorems for Set-valued Denjoy-pettis Integrable Mappings

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued DenjoyPettis integrable mappings.

Best Proximity Pairs Theorems for Continuous Set-Valued Maps