Orthogonality of skew type and characterization of inner product spaces

IF 0.9 Q2 MATHEMATICS

Arabian Journal of Mathematics Pub Date : 2024-11-20 DOI:10.1007/s40065-024-00483-y

Jinyu Xia, Qi Liu, Yuxin Wang, Wenhui Xu, Yongmo Hu, Yongjin Li

引用次数: 0

Abstract

In this paper, we investigate the generalization of Hermite-Hadamard-type orthogonality within skew structures. Moslehian and Rassias (Commun Math Anal 8:16–21, 2010) characterized inner product spaces by employing the parallelogram law for skew structures in their research. We introduce the concept of skew orthogonality by integrating the parallelogram law of skew structures with Hermite-Hadamard-type orthogonality and discuss its properties. Finally, we characterize inner product spaces using mappings that preserve skew orthogonality.

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斜型的正交性与内积空间的刻划

本文研究了斜结构中hermite - hadamard型正交性的推广。Moslehian和Rassias （common Math Anal 8:16-21, 2010）在他们的研究中采用了倾斜结构的平行四边形定律来表征内积空间。将斜结构的平行四边形规律与hermite - hadamard型正交性相结合，引入了斜正交的概念，并讨论了其性质。最后，我们使用保持斜正交的映射来描述内积空间。

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

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.