In this paper, we investigate the properties of neighbourhoods of functions for the classes U CV (α) and Sp(α). First we established an inclusion relationship between them and proved a necessary and sufficient condition interms of convolutions for a function f to be in Sp(α). Next we show that the class Sp(α) is closed under convolution with functions f (z) which are convex univalent. The resul...

We prove that if Y is a closed subspace of a Banach space X such that Y and X/Y admit an equivalent asymptotically uniformly smooth norm, then X also admits an equivalent asymptotically uniformly smooth norm. The proof is based on the use of the Szlenk index and yields a few other applications to renorming theory.

The dual of the James Tree space is asymptotically uniformly convex.

and Applied Analysis 3 In this paper, we generalize and modify the iteration of Abbas et al. 7 from two mapping to the infinite family mappings {Ti : i ∈ N} of multivalued quasi-nonexpansive mapping in a uniformly convex Banach space. Let {Ti} be a countable family of multivalued quasi-nonexpansive mapping from a bounded and closed convex subset K of a Banach space into P K with F : ⋂∞ i 1 F Ti...