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Dergiler / Journal of Universal Mathematics / 2026 / Cilt: 9 Sayı: 1

A GENERALIZATION OF CONTRACTION MAPPING THEOREMS IN A NEWLY DEFINED GENERALIZED METRIC SPACE

Mohammad Irshad Khodabocus(University of Mauritius)0000-0003-2252-4342
Noor-Ul-Hacq Sookıa(University of Mauritius)0000-0002-3155-0473
Sayfa
18–35
Yayın Tarihi
2026-06-20
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-axioms and $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-spaces are classified, an illustrative application is presented, highlighting some $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-properties, and the work is concluded.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:A newly defined generalized metric space, called \emph{$\varrho_{\mathfrak{g}}$-space} and denoted by $\mathfrak{M}_{\mathfrak{g}}=\left(\Sigma,\varrho_{\mathfrak{g}}\right)$, is introduced axiomatically and various $\varrho_{\mathfrak{g}}$-concepts as \emph{$\varrho_{\mathfrak{g}}$-fundamental sequence}, \emph{$\varrho_{\mathfrak{g}}$-convergence}, \emph{$\varrho_{\mathfrak{g}}$-contraction mapping}, and \emph{$\varrho_{\mathfrak{g}}$-fixed point} are defined in the $\varrho_{\mathfrak{g}}$-space, analogous to those in $\varrho_{\mathfrak{o}}$-spaces.
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Temel Bulgular & Veri:Thereafter, a generalized contraction mapping theorem called \textit{$\varrho_{\mathfrak{g}}$-contraction mapping theorem} is presented in the $\varrho_{\mathfrak{g}}$-space, founding its statement and proof on these $\varrho_{\mathfrak{g}}$-concepts.
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Sonuç & Katkı:Finally, $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-axioms and $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-spaces are classified, an illustrative application is presented, highlighting some $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-properties, and the work is concluded.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$\mathfrak{g}$-metric · $\varrho_{\mathfrak{g}}$-space · $\varrho_{\mathfrak{g}}$-fundamental sequence

Özet

A newly defined generalized metric space, called \emph{$\varrho_{\mathfrak{g}}$-space} and denoted by $\mathfrak{M}_{\mathfrak{g}}=\left(\Sigma,\varrho_{\mathfrak{g}}\right)$, is introduced axiomatically and various $\varrho_{\mathfrak{g}}$-concepts as \emph{$\varrho_{\mathfrak{g}}$-fundamental sequence}, \emph{$\varrho_{\mathfrak{g}}$-convergence}, \emph{$\varrho_{\mathfrak{g}}$-contraction mapping}, and \emph{$\varrho_{\mathfrak{g}}$-fixed point} are defined in the $\varrho_{\mathfrak{g}}$-space, analogous to those in $\varrho_{\mathfrak{o}}$-spaces. Thereafter, a generalized contraction mapping theorem called \textit{$\varrho_{\mathfrak{g}}$-contraction mapping theorem} is presented in the $\varrho_{\mathfrak{g}}$-space, founding its statement and proof on these $\varrho_{\mathfrak{g}}$-concepts. From the theorem, propositions concerning \textit{$\varrho_{\mathfrak{g}}$-contraction mapping error estimates} and the \textit{implication between $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-spaces} are derived. Then, a corollary concerning the implication between $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-contraction mappings and the implication between $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-fixed points are given. Finally, $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-axioms and $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-spaces are classified, an illustrative application is presented, highlighting some $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-properties, and the work is concluded.

Abstract

A newly defined generalized metric space, called \emph{$\varrho_{\mathfrak{g}}$-space} and denoted by $\mathfrak{M}_{\mathfrak{g}}=\left(\Sigma,\varrho_{\mathfrak{g}}\right)$, is introduced axiomatically and various $\varrho_{\mathfrak{g}}$-concepts as \emph{$\varrho_{\mathfrak{g}}$-fundamental sequence}, \emph{$\varrho_{\mathfrak{g}}$-convergence}, \emph{$\varrho_{\mathfrak{g}}$-contraction mapping}, and \emph{$\varrho_{\mathfrak{g}}$-fixed point} are defined in the $\varrho_{\mathfrak{g}}$-space, analogous to those in $\varrho_{\mathfrak{o}}$-spaces. Thereafter, a generalized contraction mapping theorem called \textit{$\varrho_{\mathfrak{g}}$-contraction mapping theorem} is presented in the $\varrho_{\mathfrak{g}}$-space, founding its statement and proof on these $\varrho_{\mathfrak{g}}$-concepts. From the theorem, propositions concerning \textit{$\varrho_{\mathfrak{g}}$-contraction mapping error estimates} and the \textit{implication between $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-spaces} are derived. Then, a corollary concerning the implication between $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-contraction mappings and the implication between $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-fixed points are given. Finally, $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-axioms and $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-spaces are classified, an illustrative application is presented, highlighting some $\varrho_{\mathfrak{o}}$, $\varrho_{\mathfrak{g}}$-properties, and the work is concluded.

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Bu Makaleye Atıf Yap

Khodabocus, M. I., Sookıa, N. (2026). A GENERALIZATION OF CONTRACTION MAPPING THEOREMS IN A NEWLY DEFINED GENERALIZED METRIC SPACE. Journal of Universal Mathematics, Cilt: 9 Sayı: 1, 18–35. https://doi.org/10.33773/jum.1897212

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