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Refined Stability Results of Functional Equation in Four Variables

이순|김학만
경북대학교 자연과학대학 수학과|2015.03|Kyungpook Mathematical Journal|제55권 제1호|pp. 73-81|DOI http://dx.doi.org/10.5666/KMJ.2015.55.1.73

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참고문헌

키워드

Hyers-Ulam stabilityquadratic functional equation
주제분류수학

초록

In this paper, we present the general solution of the functional equation rf( x + y + z + w s ) + rf( x + y - z - w s ) + rf( x - y + z - w s ) + rf( x - y - z + w s ) = tf (x) + tf (y) + tf(z) + tf(w) and improve the Hyers{Ulam stability of the equation.

Abstract

In this paper, we present the general solution of the functional equation rf( x + y + z + w s ) + rf( x + y - z - w s ) + rf( x - y + z - w s ) + rf( x - y - z + w s ) = tf (x) + tf (y) + tf(z) + tf(w) and improve the Hyers{Ulam stability of the equation.

참고문헌 (12)

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  6. D. H. Hyers, "On the stability of the linear functional equation", Proc. Natl. Acad. Sci. U. S. A, 27, pp.222~224 (1941)
  7. Sang Han Lee, "Hyers-Ulam-Rassias stability of a quadratic type functionalequation", 대한수학회보, 40(2), pp.183~193 (2003), 대한수학회
  8. S. Lee., "Hyers-Ulam-Rassias stability of a functional equation in three variables", J. Chungcheong Math. Soc, 16(2), pp.11~21 (2003)
  9. Chun-Gil Park, "Hyers-Ulam-Rassias Stability of an Even Functional Equation in Four Variables", Kyungpook Mathematical Journal, 44(2), pp.299~304 (2004), 경북대학교 자연과학대학 수학과
  10. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  11. F. Skof, "Proprieta locali e approssimazione di operatori", Rend. Sem. Mat. Fis. Milano, 53, pp.113~129 (1983)
  12. S. M. Ulam, "A Collection of the Mathematical Problems" (1960), Interscience Publ

관련 논문AI추천

STABILITY OF A FUNCTIONAL EQUATION DERIVING FROM QUARTIC AND ADDITIVE FUNCTIONSMadjid Eshaghi Gordji대한수학회 · 대한수학회보2010 · 제47권 제3호On the Stability of a Mixed Type Functional Equation이양희, 정순모경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제1호On the Hyers-Ulam-Rassias Stability of a General Quartic Functional Equation이양희영남수학회 · East Asian Mathematical Journal2019 · 제35권 제3호On the Stability of a Quadratic Functional EquationJae-Hyeong Bae, Kil-Woung Jun, Soon-Mo Jung경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제3호GENERALIZED HYERS–ULAM STABILITY OF ADDITIVE FUNCTIONAL EQUATIONS김학만, 손은영한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제3호ON THE STABILITY OF A BI-JENSEN FUNCTIONAL EQUATION오정하, 이양희, 전길웅한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제3호

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