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T. M. Rassias, “On the Stability of the Linear Mapping in Banach Spaces,” Proceedings of the American Mathematical Society, Vol. 72, No. 2, 1978, pp. 297-300. doi:10.1090/S0002-9939-1978-0507327-1

has been cited by the following article:

• TITLE: Hyers-Ulam-Rassias Stability for the Heat Equation

  AUTHORS: Maher Nazmi Qarawani

  KEYWORDS: Hyers-Ulam-Rassias Stability; Heat Equation; Fourier Transform; Laplace Transform

  JOURNAL NAME: Applied Mathematics, Vol.4 No.7, July 5, 2013

  ABSTRACT: In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat equation in with initial condition, in the sense of Hyers-Ulam-Rassias. We have also used Laplace transform to establish the modified Hyers-Ulam-Rassias stability of initial-boundary value problem for heat equation on a finite rod. Some illustrative examples are given.