Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Hyers-Ulam Stability of Nonlinear Integral Equation | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 927640 6 pages doi 2010 927640 Research Article Hyers-Ulam Stability of Nonlinear Integral Equation Mortaza Gachpazan and Omid Baghani Department of Applied Mathematics School of Mathematical Sciences Ferdowsi University of Mashhad Mashhad 9177948974 Iran Correspondence should be addressed to Mortaza Gachpazan gachpazan@ Received 8 April 2010 Revised 9 August 2010 Accepted 13 August 2010 Academic Editor T. Dominguez Benavides Copyright 2010 M. Gachpazan and O. Baghani. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We will apply the successive approximation method for proving the Hyers-Ulam stability of a nonlinear integral equation. 1. Introduction We say a functional equation is stable if for every approximate solution there exists an exact solution near it. In 1940 Ulam posed the following problem concerning the stability of functional equations 1 we are given a group G and a metric group G with metric p v . Given e 0 does there exist a Ỗ 0 such that if f G G satisfies p J xy f x f yy 0 for all x y e G then a homomorphism h G G exists with p f x h x e for all x e G The problem for the case of the approximately additive mappings was solved by Hyers 2 when G and G are Banach space. Since then the stability problems of functional equations have been extensively investigated by several mathematicians cf. 3-5 . Recently Y. Li and L. Hua proved the stability of Banach s fixed point theorem 6 . The interested reader can also find further details in the book of Kuczma see 7 chapter XVII . Examples of some recent developments discussions and critiques of that idea of stability can be found for example in 8-12 . 2 Fixed Point Theory and Applications In this paper we study the Hyers-Ulam stability .
