Generalized rectangular constant in Banach spaces

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2024-07-03 DOI:10.1007/s10476-024-00034-9

H. Xie, Y. Fu, Y. Li

引用次数: 0

Abstract

This paper presents two new geometric constants \(\mu(X,a)\) and \(\mu'(X,a)\), which extend the rectangular constants \(\mu(X)\) and \(\mu'(X)\). We firstly provide their bounds. Then the relationships between these geometric constants and the geometric properties of Banach spaces are discussed, including uniform nonsquareness, uniform convexity and uniform smoothness. Meanwhile, we provide several estimates of \(\mu(l_p,a)\) and obtain some new upper bound estimates on \(\mu'(l_p,a)\).

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巴拿赫空间中的广义矩形常数

本文提出了两个新的几何常数（\mu(X,a)\）和（\mu'(X,a)\），它们扩展了矩形常数（\mu(X)\）和（\mu'(X)\）。我们首先给出它们的边界。然后讨论了这些几何常数与巴拿赫空间的几何性质之间的关系，包括均匀不平方性、均匀凸性和均匀平滑性。同时，我们提供了 \(\mu(l_p,a)\)的几个估计值，并得到了 \(\mu'(l_p,a)\)的一些新的上限估计值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.