论 p 高度正交性和内积空间的特征

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-10-15 DOI:10.1016/j.jmaa.2024.128964

Somaye Heidarirad, Ruhollah Jahanipur, Mahdi Dehghani

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引用次数: 0

摘要

本文介绍并研究了实规范线性空间中 p 高度正交性的概念。这种正交性概括了众所周知的辛格正交性和高度正交性。首先，我们研究了这种正交性的主要性质。然后，举出各种例子来说明 p 高度正交性与之前定义的其他正交性（如等腰、辛格、高度和伯克霍夫-詹姆斯）之间的关系。此外，我们还研究了这一新的正交概念的存在性。特别是，我们建立了 α 存在性，并得到了 α 值的一些有趣界限。此外，根据 p 高度正交性及其与毕达哥拉斯正交性和伯克霍夫-詹姆斯正交性的关系，给出了内积空间的一些特征。

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On p-height orthogonality and characterization of inner product spaces

In this paper, we introduce and study the concept of p-height orthogonality in real normed linear spaces. This orthogonality generalizes the well-known Singer and height orthogonalities. First, we investigate main properties of this type of orthogonality. Then, variety of examples are presented to illustrate the relationship between p-height orthogonality and other previously defined (e.g., isosceles, Singer, height and Birkhoff-James) orthogonalities. Also we investigate the existence properties of this new notion of orthogonality. In particular, α-existence property is established and some interesting bounds for the values of α are obtained. Moreover, some characterizations of inner product spaces are given in terms of p-height orthogonality and its relation with Pythagorean and Birkhoff-James orthogonalities.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.