Electron. J. Diff. Equ., Vol. 2013 (2013), No. 03, pp. 1-8.

An approximation property of Gaussian functions

Soon-Mo Jung, Hamdullah Sevli, Sebaheddin Sevgin

Abstract:
Using the power series method, we solve the inhomogeneous linear first order differential equation
$$ y'(x) + \lambda (x-\mu) y(x) = \sum_{m=0}^\infty a_m (x-\mu)^m, $$
and prove an approximation property of Gaussian functions.

Submitted October 5, 2012. Published January 7, 2013.
Math Subject Classifications: 34A30, 34A40, 41A30, 39B82, 34A25.
Key Words: Linear first order differential equation; power series method; Gaussian function; approximation; Hyers-Ulam stability; local Hyers-Ulam stability.

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Soon-Mo Jung
Mathematics Section, College of Science and Technology
Hongik University, 339-701 Jochiwon, South Korea
email: smjung@hongik.ac.kr
Hamdullah Sevli
Department of Mathematics, Faculty of Sciences and Arts
Istanbul Commerce University
34672 Uskudar, Istanbul, Turkey
email: hsevli@yahoo.com
Sebaheddin Sevgin
Department of Mathematics, Faculty of Art and Science
Yuzuncu Yil University, 65080 Van, Turkey
email: ssevgin@yahoo.com

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