Research Article
Year 2025,
Volume: 6 Issue: 2, 139 - 153, 30.07.2025
Abstract
References
- Abdou N.A.A., Some fixed point theorem in modular metric space, Journal of Nonlinear Sciences and Applications, 9, 4381-4387, 2016.
- Akshoy U., Karapınar E., Erhan M.I., Fixed point theorem in complete modular metric space and an application to anti-periodic boundary value problems, Filomat, 5475-5488, 2017.
- Azadifar B., Sadeghi G., Saadati R., Park C., Integral type contractions in modular metric spaces, Journal of Inequalities and Applications, 483, 2013.
- Barman D., Sarkar K., Tiwary K., Unique common fixed point results of integral type contraction condition in 2-Banach space, The Mathematical Student, 90(1-2), 117-132, 2021.
- Chaira K., Eladraoui A., Kabil M., Extensions of some fixed point theorems for weak-contraction mapping in partially ordered modular metric spaces, Iranian Journal of Mathematical Sciences and Informatics, 15(1), 111-124, 2020.
- Chistyakov V.V., Metric modular space, I: Basics concepts, Nonlinear Analysis, Theory, Methods and Applications, 72, 1-14, 2010.
- Faried N., Ghaffar E.A.H., Hamdy S., Common fixed point theorems for several multivalued mappings on proximal sets in regular modular space, Journal of Inequalities and Applications, 129, 2021.
- Hosseini H., Eshaghi M., Fixed point results in orthogonal modular metric spaces, International Journal of Analysis and Applications, 11(2), 425-436, 2020.
- Khamsi M.A., Kozlowski W.M., Fixed Point Theory in Modular Function Space, Birkhäuser, Cham, 2015.
- Mutlu A., Özkan K., Gürdal U., Coupled fixed point theorem in partially ordered modular metric space and its application, Journal of Computational Analysis and Applications, 25(2), 207-216, 2018.
- Nakano H., Modulared Semi-Ordered Linear Spaces, Maruzen Company, 1950.
- Okeke G.A., Francis D., Sen M. de la, Some fixed point theorem for mappings satisfying rational inequality in modular metric spaces with applications, Heliyon, 6(8), 2020.
- Okeke G.A., Francis D., Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces, Arab Journal of Mathematical Sciences, 27(2), 214-234, 2021.
- Paul M., Sarkar K., Tiwary K., Fixed point theorems for integral-type weak-contraction mappings in modular metric spaces, General Mathematics, 31(1), 21-37, 2023.
Fixed Point Theorems for Generalized Integral Type Weak-Contraction Mappings in Convex Modular Metric Spaces
Abstract
Fixed point theory in convex modular metric spaces has seen significant advancements due to its broad applicability in various fields. In 2020, Chaira et al. [5] extended fixed point theorems for weak contraction mappings within partially ordered modular metric spaces. Subsequently, in 2023, Mithun et al. [14] established fixed point theorems for integral-type weak contraction mappings in modular metric spaces. Building on these foundational results, this paper investigates fixed point results for four mappings under integral-type contraction conditions in convex modular metric spaces.
Ethical Statement
The authors declare that the materials and methods used in their study do not require ethical committee and/or legal special permission.
Supporting Institution
The first author wishes to acknowledge the financial support from University Grant Commission (UGC-NET JRF).
References
- Abdou N.A.A., Some fixed point theorem in modular metric space, Journal of Nonlinear Sciences and Applications, 9, 4381-4387, 2016.
- Akshoy U., Karapınar E., Erhan M.I., Fixed point theorem in complete modular metric space and an application to anti-periodic boundary value problems, Filomat, 5475-5488, 2017.
- Azadifar B., Sadeghi G., Saadati R., Park C., Integral type contractions in modular metric spaces, Journal of Inequalities and Applications, 483, 2013.
- Barman D., Sarkar K., Tiwary K., Unique common fixed point results of integral type contraction condition in 2-Banach space, The Mathematical Student, 90(1-2), 117-132, 2021.
- Chaira K., Eladraoui A., Kabil M., Extensions of some fixed point theorems for weak-contraction mapping in partially ordered modular metric spaces, Iranian Journal of Mathematical Sciences and Informatics, 15(1), 111-124, 2020.
- Chistyakov V.V., Metric modular space, I: Basics concepts, Nonlinear Analysis, Theory, Methods and Applications, 72, 1-14, 2010.
- Faried N., Ghaffar E.A.H., Hamdy S., Common fixed point theorems for several multivalued mappings on proximal sets in regular modular space, Journal of Inequalities and Applications, 129, 2021.
- Hosseini H., Eshaghi M., Fixed point results in orthogonal modular metric spaces, International Journal of Analysis and Applications, 11(2), 425-436, 2020.
- Khamsi M.A., Kozlowski W.M., Fixed Point Theory in Modular Function Space, Birkhäuser, Cham, 2015.
- Mutlu A., Özkan K., Gürdal U., Coupled fixed point theorem in partially ordered modular metric space and its application, Journal of Computational Analysis and Applications, 25(2), 207-216, 2018.
- Nakano H., Modulared Semi-Ordered Linear Spaces, Maruzen Company, 1950.
- Okeke G.A., Francis D., Sen M. de la, Some fixed point theorem for mappings satisfying rational inequality in modular metric spaces with applications, Heliyon, 6(8), 2020.
- Okeke G.A., Francis D., Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces, Arab Journal of Mathematical Sciences, 27(2), 214-234, 2021.
- Paul M., Sarkar K., Tiwary K., Fixed point theorems for integral-type weak-contraction mappings in modular metric spaces, General Mathematics, 31(1), 21-37, 2023.
There are 14 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Operator Algebras and Functional Analysis |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | July 30, 2025 |
| Submission Date | December 9, 2024 |
| Acceptance Date | May 12, 2025 |
| Published in Issue | Year 2025 Volume: 6 Issue: 2 |
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