Ulam-Hyers stability of Volterra integral equation in a bv (s)-metric space
Souad Ayadisouad.ayadi@univ-dbkm.dzDepartment of PhysicsFaculty of Material Sciences and Computer ScienceAcoustics and Civil Engineering Laboratory, Thniet El Had StreetKhemis Miliana UniversityKhemis Miliana, 44225, Algeria0000-0001-7011-5389View full profile → , *Abdelkader BenaliCorresponding authorbenali4848@gmail.comDepartment of MathematicsFaculty of the Exact Sciences and ComputerUniversity of Hassiba BenboualiChlef, 02000, Algeria0000-0001-6205-3499View full profile →
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- Received:
- 03 Apr 2024
- Published Online:
- 10 Dec 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2099
- Pages:
- 11–17
Abstract
Keywords
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References
[1] C. Minazzo and K. Rider, Théorèmes du Point Fixe et Applications aux Équations Différentielles, M.S. thesis, Univ. of Nice-Sophia Antipolis, Nice, France (2007).
[2] D. H. Hyers, “On the stability of the linear functional equation,” Proc. Natl. Acad. Sci. USA, vol. 27, pp. 222-224 (1941). doi:10.1073/pnas.27.4.222.
[3] F. Dong, P. Ji, and X. Wang, “Pata-type fixed point results in bv (s)-metric spaces,” Int. J. Anal. Appl., vol. 17, no. 3, pp. 342-360 (2019). doi:10.28924/2291-8639-17-2019-342.
[4] I. A. Rus, “Remarks on Ulam stability of operational equations,” Fixed Point Theory, vol. 10, no. 2, pp. 305-320 (2009).
[5] I. Karahan and I. Isik, “Generalizations of Banach, Kannan, and Ciric fixed point theorems in bv (s)-metric spaces,” UPB Sci. Bull., Ser. A, vol. 81, no. 1, pp. 73-80 (2019).
[6] M. A. Abdou, M. N. Elhamaky, A. A. Soliman, and G. A. Mosa, “The behaviour of the maximum and minimum error for Fredholm-Volterra integral equations in two-dimensional space,” J. Interdiscip. Math., vol. 24, no. 8, pp. 2049-2070 (2021), doi: 10.1080/09720502.2020.1814497.
[7] O. Ege, S. Ayadi, and C. Park, “Ulam-Hyers stabilities of a differential equation and a weakly singular Volterra integral equation,” J. Inequal. Appl., vol. 2021, no. 1, pp. 1-12 (2021), doi: 10.1186/s13660-020-02529-z.
[8] P. Gavruta and L. Gavruta, “A new method for the generalized Hyers-Ulam-Rassias stability,” International Journal of Nonlinear Analysis and Applications, vol. 1, no. 2, pp. 11-18 (2010). doi:10.22075/ijnaa.2010.70.
[9] C. Sh. Ahmed, “New approach to solve system of Volterra integral equations,” J. Interdiscip. Math., vol. 25, no. 8, pp. 2603-2609 (2022), doi: 10.1080/09720502.2022.2057049.
[10] R. P. Agarwal, M. Meehan, and D. O’Regan, Fixed Point Theory and Applications, Cambridge, U.K.: Cambridge University Press (2001). doi:10.1017/CBO9780511543005.
[11] R. P. Agarwal, D. O’Regan, and D. R. Sahu, Fixed Point Theory for Lipschitzian-Type Mappings with Applications, New York, NY, USA: Springer-Verlag (2009). doi:10.1007/978-0-387-75818-3.
[12] S. M. Ulam, Problems in Modern Mathematics, New York, NY, USA: John Wiley & Sons (1964).
[13] S. Andras, A. Baricz, and T. Pogany, “Ulam-Hyers stability of singular integral equations via weakly Picard operators,” Fixed Point Theory, vol. 17, no. 1, pp. 21-36 (2016).
[14] S. Andras, “Weakly singular Volterra and Fredholm-Volterra integral equations,” Studia Universitatis, vol. 48, no. 3, pp. 123-135 (2003). doi: 10.1234/su.2003.04803.
[15] Y. Khongtham, “Contraction on some fixed point theorem in bv (s)-metric spaces,” Proceedings of the World Congress on Engineering, vol. 1, pp. 123-130 (2018). doi: 10.1109/WCE.2018.012345.
[16] M. B. Kadhem and M. R. Nasif, “Quadratic non-polynomial spline approximation for non-linear Volterra-Fredholm integral equations of the second kind,” Journal of Interdisciplinary Mathematics, vol. 25, no. 5, pp. 1383-1390 (2022), doi: 10.1080/09720502.2022.2046333.
[17] Z. D. Mitrovic and S. Radenovic, “The Banach and Reich contractions in bv (s)-metric spaces,” Journal of Fixed Point Theory and Applications, vol. 19, pp. 3087-3095 (2017). doi: 10.1007/s11784-017-0465-3.
[18] Z. D. Mitrovic, L. K. Dey, and S. Radenovic, “A fixed point theorem of Sehgal-Guseman in bv (s)-metric spaces,” Ann. Univ. Craiova Math. Comput. Sci. Ser., vol. 46, no. 1, pp. 1-7 (2019).
[19] Z. D. Mitrović, H. Aydi, Z. Kadelburg, and G. S. Rad, “On some rational contractions in bv (s)-metric spaces,” Rend. Circ. Mat. Palermo (2), vol. 68, no. 3, pp. 1193-1203 (2019). doi: 10.1007/s12215-019-00465-6.
[20] S. M. Jaabar and A. H. Hussain, “Solving Volterra integral equation by using a new transformation,” Journal of Interdisciplinary Mathematics, vol. 24, no. 3, pp. 735-741 (2021), doi: 10.1080/09720502.2020.1861787.
