vol. 162, No. 2, 1991 k-β and k-Nearly Uniformly Convex Banach Spaces Denka Kutzarova Different uniform geometrical properties have been defined between the uniform convexity and the reflexivity of Banach spaces. In the present paper we introduce other properties of this type, namely k-β and k-nearly uniform convexity. The definitions, as well as some of the results presented here, are announce...

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the proposed iterative scheme under some appropriate conditions.

An analytic function f(z)= z+an+1zn+1+··· , defined on the unit disk = {z : |z|< 1}, is in the class Sp if zf ′(z)/f(z) is in the parabolic region Rew > |w −1|. This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be in Sp are obtained. In particular, we find condition on λ such that the function f(z), satisfying (1−α)(f(z)/z)μ+αf ′(z)(...

In this paper, we propose a viscosity iteration process for semigroup of asymptotically pseudocontractive mappings, and prove a strong convergence theorem in uniformly convex Banach space for the proposed iteration process.

Making use of the generalized hypergeometric functions, we introduce some generalized class of k−uniformly convex and starlike functions and for this class, we settle the Silverman’s conjecture for the integral means inequality. In particular, we obtain integral means inequalities for various classes of uniformly convex and uniformly starlike functions in the unit disc.

Absolutely representing system (ARS) in a Banach space X is a set D ⊂ X such that every vector x in X admits a representation by an absolutely convergent series x = ∑ i aixi with (ai) ⊂ R and (xi) ⊂ D. We investigate some general properties of ARS. In particular, ARS in uniformly smooth and in B-convex Banach spaces are characterized via ε-nets of the unit balls. Every ARS in a B-convex Banach ...

Making use of the Dziok-Srivastava operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.