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Extended unified interpolative and hybrid (α,β,F) contractions in metric spaces and applications to integral equations.

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Title: Extended unified interpolative and hybrid (α,β,F) contractions in metric spaces and applications to integral equations.
Authors: Zoto, Kastriot1,2 (AUTHOR) kzoto@uogj.edu.al, Moussaoui, Abdelhamid3 (AUTHOR) a.moussaoui@usms.ma, Radenović, Stojan4 (AUTHOR) radens@beotel.net
Source: Fixed Point Theory & Algorithms for Sciences & Engineering. 3/30/2026, Vol. 2026 Issue 1, p1-17. 17p.
Subjects: Contraction operators, Integral equations, Nonlinear analysis, Metric spaces, Mathematical mappings, Uniqueness (Mathematics), Fixed point theory
Abstract: This paper develops a unified and extended framework for contraction-type mappings in metric spaces by introducing extended unified interpolative Ćirić–Reich–Rus type (α , β , F) -contractions together with their r-order counterparts. Within this general setting, rigorous existence and uniqueness results for fixed points of self-mappings are established. The proposed approach not only subsumes numerous classical and contemporary contraction principles as particular cases, but also elucidates the structural relationships among them. The scope and effectiveness of the new framework are further demonstrated through applications to nonlinear integral equations, confirming its relevance and potential for broader analytical investigations. [ABSTRACT FROM AUTHOR]
Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Extended unified interpolative and hybrid (α,β,F) contractions in metric spaces and applications to integral equations.
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  Data: This paper develops a unified and extended framework for contraction-type mappings in metric spaces by introducing extended unified interpolative Ćirić–Reich–Rus type (α , β , F) -contractions together with their r-order counterparts. Within this general setting, rigorous existence and uniqueness results for fixed points of self-mappings are established. The proposed approach not only subsumes numerous classical and contemporary contraction principles as particular cases, but also elucidates the structural relationships among them. The scope and effectiveness of the new framework are further demonstrated through applications to nonlinear integral equations, confirming its relevance and potential for broader analytical investigations. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1186/s13663-026-00832-w
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        Text: English
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      – SubjectFull: Nonlinear analysis
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      – SubjectFull: Metric spaces
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              Text: 3/30/2026
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