Fixed point theorems for generalized Lipschitzian semigroups are proved in puniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp , and in Sobolev spaces Hk,p , for 1<p <∞ and k≥ 0.

This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.

We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of c0 and superreflexivity are discussed. The question of coarse embeddability into uniformly convex Banach spaces became interesting after the recent work of G. Kasparov and G. Yu, who showed the coarse Novi...

Let X be a normed linear space, and let S(X) = fx 2 X : kxk = 1g be the unit sphere of X. Brodskii and Milman 1] introduced the following geometric concept: Deenition 1. A bounded, convex subset K of a Banach space X is said to have normal structure if every convex subset H of K that contains more than one point contains a point x 0 2 H, such that supfkx 0 ? yk : y 2 Hg < d(H); where d(H) = sup...

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the ...

We propose the class of uniformly convex W -hyperbolic spaces with monotone modulus of uniform convexity (UCW -hyperbolic spaces for short) as an appropriate setting for the study of nonexpansive iterations. UCW -hyperbolic spaces are a natural generalization both of uniformly convex normed spaces and CAT (0)-spaces. Furthermore, we apply proof mining techniques to get effective rates of asympt...

The concept of uniform convexity of a Banach space was generalized to linear operators between Banach spaces and studied by Beauzamy [1]. Under this generalization, a Banach space X is uniformly convex if and only if its identity map IX is. Pisier showed that uniformly convex Banach spaces have martingale type p for some p > 1. We show that this fact is in general not true for linear operators....

We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of c0 and superreflexivity are discussed. The question of coarse embeddability into uniformly convex Banach spaces became interesting after the recent work of G. Kasparov and G. Yu, who showed the coarse Novi...