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<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_493_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\textbf {o}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">o</mi> </math></EquationSource> </InlineEquation>-inequalities which are a natural generalization of the triangle inequality, and the construction of which leads to the notion of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_493_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\textbf {o}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">o</mi> </math></EquationSource> </InlineEquation>-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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月14日

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  • Hallowed Oluwadara Olaoluwa,
  • Aminat Olawunmi Ige,
  • Johnson Olajire Olaleru

摘要

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 \({{\textbf {o}}}\) o -inequalities which are a natural generalization of the triangle inequality, and the construction of which leads to the notion of \({{\textbf {o}}}\) 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.