CRR-$ P $-type and $ F $-$ P $-type contractions in $ b $-metric spaces

Oğuz Solak; Duran Türkoğlu; Müzeyyen Sangurlu Sezen; Oğuz Solak; Duran Türkoğlu; Müzeyyen Sangurlu Sezen

doi:10.3934/math.2026829

AIMS Mathematics

2026, Volume 11, Issue 7: 20407-20422. doi: 10.3934/math.2026829

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Research article

CRR-$ P $-type and $ F $-$ P $-type contractions in $ b $-metric spaces

1.
Graduate School of Natural and Applied Sciences, Gazi University, Ankara, Turkey; oguz.solak@gazi.edu.tr
2.
Department of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey; dturkoglu@gazi.edu.tr, muzeyyensangurlu@gazi.edu.tr

Received: 07 May 2026 Revised: 27 June 2026 Accepted: 29 June 2026 Published: 13 July 2026
MSC : 47H10, 54H25

This research introduced two new contraction mappings by integrating $ \psi $-modified interpolative Ćirić-Reich-Rus-type and $ F $-contractions with the recently established $ P $-contraction framework. Specifically, the concepts of $ \psi $-modified interpolative Ćirić-Reich-Rus-$ P $-type and $ F $-$ P $-type contractions were formulated. Existence and uniqueness theorems for fixed points regarding these mappings were established within the context of complete $ b $-metric spaces. To substantiate the theoretical findings, several illustrative examples were provided. Furthermore, the practical utility of the results was demonstrated by addressing the existence and uniqueness of solutions for both a specific class of nonlinear Fredholm integral equations and nonlinear fractional differential equations.
Citation: Oğuz Solak, Duran Türkoğlu, Müzeyyen Sangurlu Sezen. CRR-$ P $-type and $ F $-$ P $-type contractions in $ b $-metric spaces[J]. AIMS Mathematics, 2026, 11(7): 20407-20422. doi: 10.3934/math.2026829

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Abstract

This research introduced two new contraction mappings by integrating $ \psi $-modified interpolative Ćirić-Reich-Rus-type and $ F $-contractions with the recently established $ P $-contraction framework. Specifically, the concepts of $ \psi $-modified interpolative Ćirić-Reich-Rus-$ P $-type and $ F $-$ P $-type contractions were formulated. Existence and uniqueness theorems for fixed points regarding these mappings were established within the context of complete $ b $-metric spaces. To substantiate the theoretical findings, several illustrative examples were provided. Furthermore, the practical utility of the results was demonstrated by addressing the existence and uniqueness of solutions for both a specific class of nonlinear Fredholm integral equations and nonlinear fractional differential equations.

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