Conditionally Compatible Mappings, Non-Compatible Mappings, Faintly Compatible Mappings and Some Results on Common Fixed Point in $C^*$-Algebra Valued Metric Space
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2025-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_717366_f53ea3e3f639b23f3c5f8f037a3e4f4a.pdf |
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| Summary: | 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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| ISSN: | 2322-5807 2423-3900 |