O-metrics: new metric-types, polygon inequalities and fixed point theorems from binary operations

IF 0.9 Q2 MATHEMATICS

Arabian Journal of Mathematics Pub Date : 2025-02-14 DOI:10.1007/s40065-025-00493-4

Hallowed Oluwadara Olaoluwa, Aminat Olawunmi Ige, Johnson Olajire Olaleru

引用次数: 0

Abstract

The class of O-metric spaces generalizes several existing metric-type spaces in literature including metric spaces, b-metric spaces, and ultra metric spaces. In this paper, we discuss the properties of the topology induced by an O-metric and establish in the setting, fixed point theorems for contractions and generalized contractions. The proofs of the theorems rely heavily on polygon \({{\textbf {o}}}\)-inequalities which are a natural generalization of the triangle inequality, and the construction of which leads to the notion of \({{\textbf {o}}}\)-series following a pattern of functions. As application, conditions for the existence of solutions of initial value problems are discussed and a generalization of Lebesgue spaces is introduced.

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o -度量：新的度量类型，多边形不等式和由二元运算得出的不动点定理

0度量空间是对文献中已有的度量空间，包括度量空间、b度量空间和超度量空间的推广。本文讨论了由0度规引起的拓扑结构的性质，并在此条件下建立了缩和广义缩的不动点定理。这些定理的证明在很大程度上依赖于多边形\({{\textbf {o}}}\) -不等式，它是三角形不等式的自然推广，它的构造导致了\({{\textbf {o}}}\) -级数遵循函数模式的概念。作为应用，讨论了初值问题解存在的条件，并推广了Lebesgue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.