Ulam stability of Volterra integral equation on a generalized metric space
DOI:
https://doi.org/10.24193/subbmath.2020.2.11Keywords:
Volterra integral equations, Ulam-Hyers stability, generalized metric space, Krasnoselski-Krein conditions, Naguno-Perron-Van Kampen conditions.Abstract
The aim of this paper is to give some Ulam-Hyers stability results for Volterra integral equations on a generalized metric space. In this case we consider the Volterra integral equation in the Krasnoselski-Krein and Naguno-Perron-Van Kampen conditions. Here we present only Ulam-Hyers stability for the Volterra integral equation.
Mathematics Subject Classification (2010): 45G10, 45M10, 47H10, 47J20.
References
Castro, L.P., Ramos, A., Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations, Banach J. Math. Anal., 3(2009), no. 1, 36-43.
C˘adariu, L., Radu, V., The fixed points method for the stability of some functional equations, Carpathian J. Math., 23(2007), no. 1-2, 63-72.
Jung, S.M., A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory and Applications, 2007, Art. ID57064, 9 pages.
Krasnoselski, M.A., Krein, S.G., Ob odnom classe theorem edinstvenosti dlia uravnenia yl = f (x, y), Uspehi Math. Nauk, 1(67), 11(1956), 209-213.
Lungu, N., Hyperbolic-type inequalities on generalized metric spaces, Carpathian J. Math., 24(2008), no. 3, 341-347.
Luxemburg, W.A.J., On the convergence of successive approximations in the theory of ordinary differential equations II, Indag. Math., 20(1958), 540-546.
Rus, A.I., Principii ¸si aplica¸tii ale teoriei punctului fix, Ed. Dacia, Cluj-Napoca, 1979. [8] Rus, A.I., Ulam stability of ordinary differential equations, Stud. Univ. Babe¸s-Bolyai Math., 54(2009), no. 4, 125-133.
Rus, A.I., Gronwall lemma approach to the Hyers-Ulam-Rassias stability of an integral equation, in: Nonlinear Analysis and Variational Problems, Springer, 2009, 147-152.
Rus, A.I., Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, 10(2009), no. 2, 305-320.
Rus, A.I., Lungu, N., Ulam stability of a nonlinear hyperbolic partial differential equation, Carpathian J. Math., 24(2008), no. 3, 403-408.
Wong, I.S.W., On the convergence of successive approximations in the Darboux problem, Ann. Polon. Math., 18(1966), 329-336.
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