Let X be an infinite-dimensional uniformly convex Banach space and let BX and SX be its closed unit ball and unit sphere, respectively. The main result of the paper is that the identity mapping on BX can be expressed as the mean of n uniformly continuous retractions from BX onto SX for every n >= 3. Then, the authors observe that the result holds under a property weaker than uniform convexity, satisfied by any complex Banach space, so that the result generalizes that of [A. Jim´enez-Vargas et al., Studia Math. 135 (1999), no. 1, 75–81; MR1686372 (2000b:46025)]. As an application the extremal structure of spaces of vector-valued uniformly continuous mappings is studied
Let X, Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed closed convex...
[Zhivkov N. V.; Живков Н. В.]For every uniformly convex Banach space X with dim X ≥ 2 there is a res...
Given a Banach space (Χ,∥ · ∥), we study the connection between uniformly convex functions f : Χ → R...
Let X be an infinite-dimensional uniformly convex Banach space and let BX and SX be its closed unit ...
AbstractWe prove a new inequality valid in any two-dimensional normed space. As an application, it i...
Abstract. The dual space X ∗ of a Banach space X is said to admit a uniformly simul-taneously contin...
In this paper, two main results concerning uniformly continuous retractions are proved. First, an $\...
For any infinite dimensional Banach space there exists a lipschitzian retraction of the closed unit ...
The concept of uniform convexity of a Banach space was gen- eralized to linear operators between Ban...
A retraction $R$ from the closed unit ball of a Banach space $X$ onto its boundary is called $k$-b...
Abstract: Let X,Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed clos...
AbstractFor a Banach space B and for a class A of its bounded closed retracts, endowed with the Haus...
summary:An infinite dimensional counterpart of uniform smoothness is studied. It does not imply refl...
AbstractWe prove an isoperimetric inequality for the uniform measure on a uniformly convex body and ...
AbstractLet X be a real Banach space with dual X∗ and moduli of convexity and smoothness δX(ε) and ϱ...
Let X, Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed closed convex...
[Zhivkov N. V.; Живков Н. В.]For every uniformly convex Banach space X with dim X ≥ 2 there is a res...
Given a Banach space (Χ,∥ · ∥), we study the connection between uniformly convex functions f : Χ → R...
Let X be an infinite-dimensional uniformly convex Banach space and let BX and SX be its closed unit ...
AbstractWe prove a new inequality valid in any two-dimensional normed space. As an application, it i...
Abstract. The dual space X ∗ of a Banach space X is said to admit a uniformly simul-taneously contin...
In this paper, two main results concerning uniformly continuous retractions are proved. First, an $\...
For any infinite dimensional Banach space there exists a lipschitzian retraction of the closed unit ...
The concept of uniform convexity of a Banach space was gen- eralized to linear operators between Ban...
A retraction $R$ from the closed unit ball of a Banach space $X$ onto its boundary is called $k$-b...
Abstract: Let X,Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed clos...
AbstractFor a Banach space B and for a class A of its bounded closed retracts, endowed with the Haus...
summary:An infinite dimensional counterpart of uniform smoothness is studied. It does not imply refl...
AbstractWe prove an isoperimetric inequality for the uniform measure on a uniformly convex body and ...
AbstractLet X be a real Banach space with dual X∗ and moduli of convexity and smoothness δX(ε) and ϱ...
Let X, Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed closed convex...
[Zhivkov N. V.; Живков Н. В.]For every uniformly convex Banach space X with dim X ≥ 2 there is a res...
Given a Banach space (Χ,∥ · ∥), we study the connection between uniformly convex functions f : Χ → R...