The Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive, and more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has an alike Bregman-Opial property for Bregman distances. In this paper, using Bregman distances, we introduce t...

A one-step iteration with errors is considered for a family of asymptotically nonexpansive nonself mappings. Weak convergence of the purposed iteration is obtained in a Banach space.

Cylindrical Wiener processes in real separable Banach spaces are defined, and an approximation theorem involving scalar Wiener processes is given for such processes. A weak stochastic integral for Banach spaces involving a cylindrical Wiener process as integrator and an operator-valued stochastic process as integrand is defined. Basic properties of this integral are stated and proved. A class o...

LetX be a complex Banach space andX∗ its dual space. We consider the topological subspace Π X { x, x∗ : x∗ x 1 ‖x‖ ‖x∗‖} of the product space BX ×BX∗ , equipped with norm and weak-∗ topology on the unit ball BX ofX and its dual unit ball BX∗ , respectively. It is easy to see that Π X is a closed subspace of BX × BX∗ . For two complex Banach spaces X and Y , denote by Cb BX : Y the Banach space ...

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak-extreme points of the unit ball is discrete.

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.