The Ptolemy constant of absolute normalized norms on R
نویسنده
چکیده
Correspondence: zuozhanfei@139. com Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China Abstract We determine and estimate the Ptolemy constant of absolute normalized norms on R by means of their corresponding continuous convex functions on [0, 1]. Moreover, the exact values were calculated in some concrete Banach spaces. 2000 Mathematics Subject Classification: 46B20.
منابع مشابه
The Ptolemy constant of absolute normalized norms on R2
Correspondence: zuozhanfei@139. com Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China Abstract We determine and estimate the Ptolemy constant of absolute normalized norms on R by means of their corresponding continuous convex functions on [0, 1]. Moreover, the exact values were calculated in some concrete Banach spaces. 2000 Mathematics Subject C...
متن کاملSome Geometric Constants of Absolute Normalized Norms on R
We consider the Banach space X = (R, ‖ · ‖) with a normalized, absolute norm. Our aim in this paper is to calculate the modified NeumannJordan constant C ′ NJ(X) and the Zbăganu constant CZ(X).
متن کاملThe James Constant of Normalized Norms on R2
We introduce a new class of normalized norms on R 2 which properly contains all absolute normalized norms. We also give a criterion for deciding whether a given norm in this class is uniformly nonsquare. Moreover, an estimate for the James constant is presented and the exact value of some certain norms is computed. This gives a partial answer to the question raised by Kato et al. under the Crea...
متن کاملEvery n-dimensional normed space is the space Rn endowed with a normal norm
A norm ‖ · ‖ on R is said to be absolute if ‖(x, y)‖ = ‖(|x|, |y|)‖ for all (x, y) ∈R, and normalized if ‖(, )‖ = ‖(, )‖ = . The set of all absolute normalized norms onR is denoted by AN. Bonsall and Duncan [] showed the following characterization of absolute normalized norms on R. Namely, the set AN of all absolute normalized norms on R is in a one-to-one correspondence with the s...
متن کاملThe 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...
متن کامل