Jung, Soon-Mo A fixed point approach to the stability of a Volterra integral equation. (English) Zbl 1155.45005 Fixed Point Theory Appl. 2007, Article ID 57064, 9 p. (2007). The author uses a fixed point method for proving the Hyers-Ulam-Rassias stability of a Volterra integral equation of the second kind. Reviewer: B. G. Pachpatte (Aurangabad) Cited in 2 ReviewsCited in 20 Documents MSC: 45M10 Stability theory for integral equations 45G10 Other nonlinear integral equations Keywords:fixed point method; Hyers-Ulam-Rassias stability; Volterra integral equation of the second kind PDF BibTeX XML Cite \textit{S.-M. Jung}, Fixed Point Theory Appl. 2007, Article ID 57064, 9 p. (2007; Zbl 1155.45005) Full Text: DOI EuDML References: [1] Ulam SM: A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8. Interscience, New York, NY, USA; 1960:xiii+150. [2] Hyers DH: On the stability of the linear functional equation.Proceedings of the National Academy of Sciences of the United States of America 1941,27(4):222-224. 10.1073/pnas.27.4.222 · Zbl 0061.26403 [3] Rassias ThM: On the stability of the linear mapping in Banach spaces.Proceedings of the American Mathematical Society 1978,72(2):297-300. 10.1090/S0002-9939-1978-0507327-1 · Zbl 0398.47040 [4] Forti GL: Hyers-Ulam stability of functional equations in several variables.Aequationes Mathematicae 1995,50(1-2):143-190. 10.1007/BF01831117 · Zbl 0836.39007 [5] Găvruţa P: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings.Journal of Mathematical Analysis and Applications 1994,184(3):431-436. 10.1006/jmaa.1994.1211 · Zbl 0818.46043 [6] Hyers DH, Isac G, Rassias ThM: Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and Their Applications. Volume 34. Birkhäuser, Boston, Mass, USA; 1998:vi+313. [7] Hyers DH, Rassias ThM: Approximate homomorphisms.Aequationes Mathematicae 1992,44(2-3):125-153. 10.1007/BF01830975 · Zbl 0806.47056 [8] Jung S-M: Hyers-Ulam-Rassias stability of functional equations.Dynamic Systems and Applications 1997,6(4):541-565. · Zbl 0891.39025 [9] Jung S-M: Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis. Hadronic Press, Palm Harbor, Fla, USA; 2001:ix+256. · Zbl 0980.39024 [10] Rassias ThM: On the stability of functional equations and a problem of Ulam.Acta Applicandae Mathematicae 2000,62(1):23-130. 10.1023/A:1006499223572 · Zbl 0981.39014 [11] Diaz JB, Margolis B: A fixed point theorem of the alternative, for contractions on a generalized complete metric space.Bulletin of the American Mathematical Society 1968, 74: 305-309. 10.1090/S0002-9904-1968-11933-0 · Zbl 0157.29904 [12] Cădariu, L.; Radu, V., On the stability of the Cauchy functional equation: a fixed point approach, No. 346, 43-52 (2004), Graz, Austria · Zbl 1060.39028 [13] Cădariu L, Radu V: Fixed points and the stability of Jensen’s functional equation.Journal of Inequalities in Pure and Applied Mathematics 2003,4(1, article 4):1-7. · Zbl 1043.39010 [14] Jung S-M: A fixed point approach to the stability of isometries.Journal of Mathematical Analysis and Applications 2007,329(2):879-890. 10.1016/j.jmaa.2006.06.098 · Zbl 1153.39309 [15] Radu V: The fixed point alternative and the stability of functional equations.Fixed Point Theory 2003,4(1):91-96. · Zbl 1051.39031 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.