Weak compactness and the Eisenfeld-Lakshmikantham measure of nonconvexity

Weak Compactness of the Set of ε-Extensions

New operators through measure of non-compactness

In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...

Dependent Choices and Weak Compactness

We work in set-theory without the Axiom of Choice ZF. We prove that the principle of Dependent Choices (DC) implies that the closed unit ball of a uniformly convex Banach space is weakly compact, and in particular, that the closed unit ball of a Hilbert space is weakly compact. These statements are not provable in ZF, and the latter statement does not imply DC. Furthermore, DC does not imply th...

Smoothness and Weak* Sequential Compactness

If a Banach space E has an equivalent smooth norm, then every bounded sequence in E* has a weak* converging subsequence. Generalizations of this result are obtained.

weak compactness of the set of ε-extensions