Approximate Fixed-Point Results for Partial α,μ,ψ,h,F-Generalized Hardy and Rogers Convex Contraction Mappings of Type 2 in b-Metric Spaces With Applications

Semira H. Alemu and Kidane K. Tola

Abstract and Applied Analysis, 2026, vol. 2026, 1-16

Abstract: This paper aims to prove approximate fixed-point and fixed-point results for new classes of generalized Hardy and Rogers convex contraction mappings of type 2. To develop our main results, we apply an auxiliary function, which may not be continuous, and integrate the concepts of Hardy and Rogers convex contraction mappings with the upclass of Type I functions. Using admissibility conditions, the proposed framework relaxes the continuity and completeness assumptions of related fixed-point results to comparatively less restrictive assumptions, namely α,μ-continuity and α,μ-completeness, respectively. This work provides a new direction in the study of approximate fixed points as well as fixed points by broadening the scope of Hardy and Rogers convex contraction mappings of type 2. We further illustrate the applicability of our results by providing supportive examples and applications to graph theory and fractional calculus. In the context of b-metric spaces, our results extend and generalize several existing findings in the literature.MSC2020 Classification: 47H10, 54H25.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:9101054

DOI: 10.1155/aaa/9101054

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