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ON COMMON FIXED POINTFOR $\alpha-\psi-$ CONTRACTIVE MAPPINGSIN $\Phi$-METRIC SPACES
Keywords:
F-metric space, Common fixed point, admissible, ContractionDOI:
https://doi.org/10.17654/0972087126015Abstract
This study aims to establish the existence and uniqueness of common fixed points for two self-mappings in the setting of $\Phi$-metric spaces. By employing the concept of $\alpha$-admissibility, a generalized $\alpha-\psi-S-$ contractive mapping, which commutes with a self-mapping $\$$, and a pair of $\alpha-\psi$-contractive mappings is introduced. Several common fixed point theorems are derived under suitable conditions. These results generalize and extend common fixed point theorems previously established in standard metric and $\Phi$-metric framework. Furthermore, we demonstrate that $\alpha$-admissibility allows the determination of common fixed points for discontinuous mappings. Several illustrative examples are included to validate our findings.
Received: June 19, 2025
Accepted: August 29, 2025
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