• Title/Summary/Keyword: rectangular b-metric spaces

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FIXED POINT RESULTS IN SOFT RECTANGULAR b-METRIC SPACE

  • Sonam;C. S. Chauhan;Ramakant Bharadwaj;Satyendra Narayan
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.3
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    • pp.753-774
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    • 2023
  • The fundamental aim of the proposed work is to introduce the concept of soft rectangular b-metric spaces, which involves generalizing the notions of rectangular metric spaces and b-metric spaces. Furthermore, an investigation into specific characteristics and topological aspects of the underlying generalization of metric spaces is conducted. Moreover, the research establishes fixed point theorems for mappings that satisfy essential criteria within soft rectangular b-metric spaces. These theorems offer a broader perspective on established results in fixed point theory. Additionally, several congruous examples are presented to enhance the understanding of the introduced spatial framework.

FIXED POINT THEOREMS IN CONTROLLED RECTANGULAR METRIC SPACES

  • Mohamed Rossafi;Abdelkarim Kari
    • The Pure and Applied Mathematics
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    • v.30 no.2
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    • pp.169-190
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    • 2023
  • In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality in the definition of a metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.

SOME FIXED POINT THEOREMS FOR GENERALIZED KANNAN TYPE MAPPINGS IN RECTANGULAR b-METRIC SPACES

  • Rossafi, Mohamed;Massit, Hafida
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.3
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    • pp.663-677
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    • 2022
  • This present paper extends some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Kannan type mappings. Non-trivial examples are further provided to support the hypotheses of our results.

SOME RESULTS OF GENERALIZED HARDY-ROGER MAPPINGS IN RECTANGULAR b-METRIC SPACES

  • Chatuphol Khaofong;Phachara Saipara;Anantachai Padcharoen
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.4
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    • pp.1097-1113
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    • 2023
  • In this paper, we extend some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Hardy-Roger type mappings. Our result generalizes many known results in fixed point theory. Finally, we offer a example to illustrate our result.

𝛿-CONVEX STRUCTURE ON RECTANGULAR METRIC SPACES CONCERNING KANNAN-TYPE CONTRACTION AND REICH-TYPE CONTRACTION

  • Sharma, Dileep Kumar;Tiwari, Jayesh
    • The Pure and Applied Mathematics
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    • v.29 no.4
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    • pp.293-306
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    • 2022
  • In the present paper, we introduce the notation of 𝛿-convex rectangular metric spaces with the help of convex structure. We investigate fixed point results concerning Kannan-type contraction and Reich-type contraction in such spaces. We also propound an ingenious example in reference of given new notion.

A COMMON FIXED POINT THEOREM FOR T-CONTRACTIONS ON GENERALIZED CONE b-METRIC SPACES

  • Rangamma, Manhala;Reddy, Pagidi Mallikarjun
    • Communications of the Korean Mathematical Society
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    • v.32 no.1
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    • pp.65-74
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    • 2017
  • In this paper, we establish a unique common fixed point theorem for T-contraction of two self maps on generalized cone b-metric spaces with solid cone. The result of this paper improves and generalizes several well-known results in the literature. Two examples are also given to support the result.