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ON THE STABILITY OF A BI-JENSEN FUNCTIONAL EQUATION  

Jun, Kil-Woung (DEPARTMENT OF MATHEMATICS, CHUNGNAM NATIONAL UNIVERSITY)
Lee, Yang-Hi (DEPARTMENT OF MATHEMATICS EDUCATION, GONGJU NATIONAL UNIVERSITY OF EDUCATION)
Oh, Jeong-Ha (DEPARTMENT OF MATHEMATICS, CHUNGNAM NATIONAL UNIVERSITY)
Publication Information
The Pure and Applied Mathematics / v.17, no.3, 2010 , pp. 231-247 More about this Journal
Abstract
In this paper, we investigate the generalized Hyers-Ulam stability of a bi-Jensen functional equation $4f(\frac{x\;+\;y}{2},\;\frac{z\;+\;w}{2})$ = f(x, z) + f(x, w) + f(y, z) + f(y, w). Also, we establish improved results for the stability of a bi-Jensen equation on the punctured domain.
Keywords
solution; stability; bi-Jensen mapping; functional equation;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Th. M. Rassias : On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72 (1978), 297-300.   DOI   ScienceOn
2 S. M. Ulam : A Collection of Mathematical Problems. Interscience Publ., New York, 1960.
3 S.-M. Jung: On the Hyers-Ulam stability of the functional equations that have the quadratic property. J. Math. Anal. Appl. 222 (1998), 126-137.   DOI   ScienceOn
4 Pl. Kannappan : Quadratic functional equation and inner product spaces. Results Math. 27 (1995), 368-372.   DOI
5 G.-H. Kim : On the stability of the quadratic mapping in normed spaces. Internat. J. Math. Math. Sci. 25 (2001), 217-229.   DOI
6 G.-H. Kim, Y.-H. Lee & D.-W. Park : On the Hyers-Ulam stability of a bi-Jensen functional equation.s. AIP Conf. Proc.1046 (2008), 99-101.
7 H.-M. Kim : A result concerning the stability of some difference equations and its applications. Indian Acad. Sci. Math. Sci. 112 (2002), 453-462.   DOI
8 J.-H. Bae and W.-G. Park : On the solution of a bi-Jensen functional equation and its stability. Bull. Korean Math. Soc. 43(2006), 499-507   과학기술학회마을   DOI
9 C.-G. Park : A generalized Jensen's mapping and linear mappings between Banach modules. Bull. Braz. Math. Soc. 36 (2005), 333-362.   DOI   ScienceOn
10 W.-G. Park & J.-H. Bae : On a Cauchy-Jensen functional equation and its stability. J. Math. Anal. Appl. 323 (2006), 634-643.   DOI   ScienceOn
11 I.-S. Chang and H.-M. Kim : Hyers-Ulam-Rassias stability of a quadratic functional equation. Kyungpook Math. J. 42(2002), 71-86   과학기술학회마을
12 P. Gavruta : A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184 (1994), 431-436.   DOI   ScienceOn
13 D. H. Hyers : On the stability of the linear functional equation. Proc. Natl. Acad. Sci. 27 (1941), 222-224.   DOI   ScienceOn
14 S.-M. Jung : Hyers-Ulam-Rassias stability of Jensen's equation and its application. Proc. Amer. Math. Soc. 126 (1998), 3137-3143.   DOI   ScienceOn
15 K.-W. Jun, Y.-H. Lee & J.-H. Oh : On the Rassias stability of a bi-Jensen functional equation. J. Math. Inequal. 2 (2008), 363-375