Show simple item record

dc.contributor.authorJanfada, Mohammad
dc.contributor.authorSadeghi, Gh.
dc.description.abstractIn this paper, the Hyers-Ulam stability of the Volterra integrodifferential equation and the Volterra equation on the finite interval [0, T], T > 0, are studied, where the state x(t) take values in a Banach space X.pl_PL
dc.publisherŁódź University Presspl_PL
dc.relation.ispartofseriesActa Universitatis Lodziensis. Folia Mathematica;1
dc.rightsUznanie autorstwa-Bez utworów zależnych 3.0 Polska*
dc.rightsUznanie autorstwa-Bez utworów zależnych 3.0 Polska*
dc.subjectHyers-Ulam stabilitypl_PL
dc.subjectVolterra integrodifferential equationpl_PL
dc.subjectVolterra equationpl_PL
dc.subjectC 0 - semigrouppl_PL
dc.titleStability of the Volterra Integrodifferential Equationpl_PL
dc.rights.holder© 2013 for University of Łódź Presspl_PL
dc.contributor.authorAffiliationDepartment of Pure Mathematics, Ferdowsi University of Mashhad Mashhad, P.O. Box 1159-91775, Iranpl_PL
dc.contributor.authorAffiliationDepartment of Mathematics, Hakim Sabzevary University Sabzevar, P.O. Box 397, Iranpl_PL
dc.referencesA. F. Bachurskaya, Uniqueness and convergence of successive approximations for a class of Volterra equations, Differentsial’nye Uraveniya 10(9) (1974), pp. 1722- 1724.pl_PL
dc.referencesL. Cădariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, in Iteration Theory (ECIT Š02), vol. 346 of Grazer Math. Ber., pp. 43-52, Karl-Franzens-Univ. Graz, Graz, Austria, 2004.pl_PL
dc.referencesL. Cădariu and V. Radu, Fixed points and the stability of Jensen’s functional equa- tion, J. Inequal. Pure Appl. Math., 4, no. 1, Art. 4 (2003).pl_PL
dc.referencesA. Constantin, Topological transversality: Application to an integrodifferential equa- tion, J. Math. Anal. Appl. 197 (1996), pp. 855-863.pl_PL
dc.referencesC. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1993.pl_PL
dc.referencesS. Czerwik, Stability of Functional Equations of Ulam–Hyers–Rassias Type, Hadronic Press, Palm Harbor, Florida, 2003.pl_PL
dc.referencesK.J. Engle and R. Nagle, One-parameter Semigroups for Linear Evaluation Equa- tions, Springer-Verlag, New York 2000.pl_PL
dc.referencesG.L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequa- tiones Math. 50 , no. 1-2 (1995), pp. 143-190.pl_PL
dc.referencesD.H. Hyers and Th.M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), pp. 125-153.pl_PL
dc.referencesD.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Basel, 1998.pl_PL
dc.referencesS.-M. Jung, A fixed point approach to the stability of isometries, J. Math. Anal. Appl., 329, no. 2(2007), pp. 879-890.pl_PL
dc.referencesS.-M. Jung, A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory Appl., 2007, Art. ID 57064, 9 pp.pl_PL
dc.referencesS.-M. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press lnc., Palm Harbor, Florida, 2001.pl_PL
dc.referencesM. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equa- tions, Pergamon Press, Oxford, 1964.pl_PL
dc.referencesM. Kwapisz, On the existence and uniqueness of solutions of a certain integral- func- tional equation, Ann. Polon. Math. 31 (1975), pp. 23-41.pl_PL
dc.referencesB. Margolits and J. Diaz, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), pp. 305-309.pl_PL
dc.referencesR. K. Miller, Nonlinear Volterra Integral Equations, W. A. Benjamin, Menlo Park, CA, 1971.pl_PL
dc.referencesB. G. Pachpatte, Inequalities for Differential and Integral Equations, Academic Press, New York, 1998.pl_PL
dc.referencesB. G. Pachpatte, On a certain iterated Volterra integrodifferential equation, An. Sti. Univ. Al. I. Cuza Iasi, Tomul LIV (2008), pp. 175-186.pl_PL
dc.referencesB. G. Pachpatte, On certain Volterra integral and Volterra integrodifferential equa- tions, Facta Univ., Ser. Math. Inform. 23, (2008), pp. 1-12.pl_PL
dc.referencesA. Pazy, Semigroups of Operators and Applications to Partial Differential Equations, Springer-Verlag, New York 1983.pl_PL
dc.referencesV. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4, no. 1 (2003), pp. 91-96.pl_PL
dc.referencesTh. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62, no. 1(2000), pp. 23-130.pl_PL
dc.referencesTh. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Aca- demic Publishers, Dordrecht, Boston and London, 2003.pl_PL
dc.referencesR. Saadati, S. M. Vaezpour, and B. E. Rhoades , T-Stability Approach to Variational Iteration Method for Solving Integral Equations, Fixed Point Theory Appl. 2009, Art. ID 393245, 9pp.pl_PL

Files in this item


This item appears in the following Collection(s)

Show simple item record

Uznanie autorstwa-Bez utworów zależnych 3.0 Polska
Except where otherwise noted, this item's license is described as Uznanie autorstwa-Bez utworów zależnych 3.0 Polska