Some inequalities concerning the James constant in Banach spaces

The retraction constant in some Banach spaces

We give new sharper estimations for the retraction constant in some Banach spaces. r 2002 Elsevier Science (USA). All rights reserved.

Some Inequalities Concerning the Weakly Convergent Sequence Coefficient in Banach Spaces

Some Results concerning Riesz Bases and Frames in Banach Spaces

In this paper, we give characterizations of Riesz bases and near Riesz bases in Banach spaces. The notion of atomic system is defined and a characterization of atomic system has been given. Also results exhibiting relationship between frames, atomic systems and Riesz bases have been proved. Further, we show that every atomic system is a projection of a Riesz basis in Banach spaces. Finally, we ...

The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...

Some inequalities concerning Smarandache's function

The objectives of this article are to study the sum IS(d) and to find some upper din bounds for Smarandache's function. This sum is proved to satisfy the inequality IS(d) ~ n at most all the composite numbers, Using this inequality, some new din upper bounds for Smarandache's function are found. These bounds improve the well-known inequality Sen) ~ n.