Conditionally Compatible Mappings, Non-Compatible Mappings, Faintly Compatible Mappings and Some Results on Common Fixed Point in C∗-Algebra Valued Metric Space

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Dhariwal Rishi; Kumar Deepak

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS (SCMA) Year:2025 | Volume:22 | Issue:1 Page(s): 109-124

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Information Journal Paper

Title

Conditionally Compatible Mappings, Non-Compatible Mappings, Faintly Compatible Mappings and Some Results on Common Fixed Point in C∗-Algebra Valued Metric Space

Author(s)

Dhariwal Rishi | Kumar Deepak | Issue Writer Certificate

Keywords

C*-algebra valued metric space

Common fixed points

E.A. property

Faintly Compatible

Non-Compatible

Abstract

This manuscript introduces and investigates various types of mappings in the context of a $C^*$-algebra valued metric space. These include conditionally compatible, non-compatible, and faintly compatible mappings. Additionally, the manuscript establishes fixed-point results for certain combinations of these mappings. Specifically, it considers pairs of self-mappings that satisfy either a $(\phi-\psi)$-Kannan-type or Chatterjea-type contractive condition and proves common fixed point theorems for faintly compatible continuous or reciprocal continuous along with non-compatible pairs of such mappings. Also, non-compatibility is relaxed by using the $E.A.$ property and faintly compatible continuous property or reciprocal continuous property for pairs of self-mappings. To demonstrate the practicality of these results, the manuscript includes examples that illustrate their usefulness.

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