A Unified Framework for Common Fixed Point Results in Suprametric Spaces with Applications to Volterra Integral Equations
DOI:
https://doi.org/10.66147/lnaa.20264275Keywords:
Common Fixed Point, Suprametric Space, Volterra Integral EquationAbstract
This paper develops a systematic common fixed point theory within the framework of suprametric spaces, a recently introduced generalization of metric spaces that accommodates a broader class of distance structures through a nonlinear relaxation of the triangle inequality. We establish several common fixed point theorems for pairs of self-mappings satisfying distinct contractive conditions, specifically Banach-type, Reich-type, Ćirić-type, and rational Gupta–Saxena type contractions, in the setting of complete suprametric spaces. Each theoretical result is accompanied by a concrete example that explicitly verifies the respective contractive hypothesis and confirms the existence and uniqueness of the common fixed point. To demonstrate the practical utility of the developed framework, the main results are applied to establish the existence and uniqueness of solutions to Volterra integral equations of the second kind, modeled via associated integral operators on the space of continuous functions endowed with a suprametric. The suprametric structure, by encompassing classical metric and b-metric spaces as special cases, renders the presented results both comprehensive in scope and broadly applicable to nonlinear problems in analysis and mathematical physics.
References
1. Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta mathematicae, 3(1), 133-181. DOI: https://doi.org/10.4064/fm-3-1-133-181
2. Kannan, R. (1968). Some results on fixed points. Bull. Cal. Math. Soc., 60, 71-76. DOI: https://doi.org/10.2307/2316437
3. Reich, S. (1971). Some remarks concerning contraction mappings. Canadian Mathematical Bulletin, 14(1), 121-124. DOI: https://doi.org/10.4153/CMB-1971-024-9
4. Chatterjea, S. K. (1972). Fixed-point theorems. Dokladi na Bolgarskata Akademiya na Naukite, 25(6), 727-730.
5. ´Ciri´c, L. B. (1972). Fixed points for generalized multi-valued contractions. Mat. Vesnik, 9(24), 265-272.
6. Hardy, G. E., & Rogers, T. D. (1973). A generalization of a fixed point theorem of Reich. Canadian Mathematical Bulletin, 16(2), 201-206. DOI: https://doi.org/10.4153/CMB-1973-036-0
7. ´Ciri´c, L. B. (1974). A generalization of Banach’s contraction principle. Proceedings of the American Mathematical Society, 45(2), 267-273. DOI: https://doi.org/10.1090/S0002-9939-1974-0356011-2
8. Berzig, M. (2022). First results in suprametric spaces with applications. Mediterranean Journal of Mathematics, 19(5), 226. DOI: https://doi.org/10.1007/s00009-022-02148-6
9. Berzig, M. (2024). Nonlinear contraction in b-suprametric spaces. The Journal of Analysis, 32(5), 2401-2414. DOI: https://doi.org/10.1007/s41478-024-00732-5
10. Panda, S. K., Agarwal, R. P., & Karapínar, E. (2023). Extended suprametric spaces and Stone-type theorem. AIMS Math, 8(10), 23183-23199. DOI: https://doi.org/10.3934/math.20231179
11. Berzig, M. (2023). Fixed point results in generalized suprametric spaces. Topological Algebra and its Applications, 11(1), 20230105. DOI: https://doi.org/10.1515/taa-2023-0105
12. Younis, M., Ahmad, H., Ozturk, M., & Singh, D. (2025). A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points. Alexandria Engineering Journal, 110, 363-375. DOI: https://doi.org/10.1016/j.aej.2024.10.001
13. Aldosari, S. J., Ahmad, H., Younis, M., Öztürk, M., & Asmat, F. (2026). Fundamental contractions in suprametric spaces: Analysis and applications. Nonlinear Analysis: Modelling and Control, 31(1), 160-177. DOI: https://doi.org/10.15388/namc.2026.31.44253
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Copyright (c) 2026 Haroon Ahmad, Mudasir Younis
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