본문 바로가기
KERD
논문KCI 등재

On the Stability of a Mixed Type Functional Equation

정순모|이양희
경북대학교 자연과학대학 수학과|2015.03|Kyungpook Mathematical Journal|제55권 제1호|pp. 91-101|DOI http://dx.doi.org/10.5666/KMJ.2015.55.1.91

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

direct methodHyers-Ulam stabilitygeneralized Hyers-Ulam stabilitymixed type functional equation
주제분류수학

초록

In this paper, we investigate the stability of the functional equation f(-x + y + z + w) + f(x - y + z + w) + f(x + y - z + w) + f(x + y + z - w) = 3f(x) + f(-x) + 3f(y) + f(-y) + 3f(z) + f(-z) + 3f(w) + f(-w) by using the direct method in the sense of Hyers.

Abstract

In this paper, we investigate the stability of the functional equation f(-x + y + z + w) + f(x - y + z + w) + f(x + y - z + w) + f(x + y + z - w) = 3f(x) + f(-x) + 3f(y) + f(-y) + 3f(z) + f(-z) + 3f(w) + f(-w) by using the direct method in the sense of Hyers.

참고문헌 (19)

  1. T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
  2. J. A. Baker, "The stability of certain functional equations", Proc. Amer. Math. Soc, 112(3), pp.729~732 (1991)
  3. L. Cadariu., "Fixed points and the stability of Jensen's functional equation", J. Inequal. Pure and Appl. Math., 4(1) (2003)
  4. L. Cadariu., "Fixed points and the stability of quadratic functional equa-tions", An. Univ. Timisoara Ser. Mat. -Inform, 41, pp.25~48 (2003)
  5. L. Cadariu., "On the stability of the Cauchy functional equation : a xed point approach", Grazer Math. Ber, 346, pp.43~52 (2004)
  6. K. Cieplinski, "Applications of xed point theorems to the Hyers-Ulam stability of functional equations-a survey", Ann. Funct. Anal, 3(1), pp.151~164 (2012)
  7. S. Czerwik, "Functional Equations and Inequalities in Several Variables" (2002), World Scienti c
  8. P. En o., "An interview with Th. M. Rassias", Banach J. Math. Anal, 1(2), pp.252~260 (2007)
  9. D. H. Hyers, "On the stability of the linear functional equation", Proc. Natl. Acad. Sci. USA, 27, pp.222~224 (1941)
  10. D. H. Hyers, "Stability of Functional Equations of Several Variables" (1998), Birkhauser
  11. S. -M. Jung, "On the Hyers-Ulam-Rassias stability of approximately additive mappings", J. Math. Anal. Appl, 204, pp.221~226 (1996)
  12. S. -M. Jung, "Hyers-Ulam-Rassias stability of Jensen's equation and its application", Proc. Amer. Math. Soc, 126, pp.3137~3143 (1998)
  13. S. -M. Jung, "On the Hyers-Ulam stability of the functional equations that have the quadratic property", J. Math. Anal. Appl, 222, pp.126~137 (1998)
  14. S.-M. Jung, "Springer Optimization and Its Applications Vol. 48" (2011), Springer
  15. M. Mirzavaziri., "A xed point approach to stability of a quadratic equation", Bull. Braz. Math. Soc. (N. S. ), 37(3), pp.361~376 (2006)
  16. M. S. Moslehian., "Stability of functional equations in non-Archimedean spaces", Appl. Anal. Discrete Math, 1(2), pp.325~334 (2007)
  17. V. Radu, "The xed point alternative and the stability of functional equations", Fixed Point Theory, 4, pp.91~96 (2003)
  18. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  19. S. M. Ulam, "Problems in Modern Mathematics" (1964), Wiley

관련 논문AI추천

On the Stability of a Quadratic Functional EquationJae-Hyeong Bae, Kil-Woung Jun, Soon-Mo Jung경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제3호On the Stability of the Functional Equation g(x+y+xy)=g(x)+f(y)+xf(y)+yg(x)정용수한국수학교육학회 · 이론수학과 교직수학2020 · 제27권 제1호Refined Stability Results of Functional Equation in Four Variables이순, 김학만경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제1호A Fixed Point Approach to the Orthogonal Stability of Mixed Type Functional Equations김창일, 전영주영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호STABILITY OF A FUNCTIONAL EQUATION DERIVING FROM QUARTIC AND ADDITIVE FUNCTIONSMadjid Eshaghi Gordji대한수학회 · 대한수학회보2010 · 제47권 제3호Stability of Mixed Type Functional Equations with Involution in Non-Archimedean Spaces김창일, 윤용식영남수학회 · East Asian Mathematical Journal2018 · 제34권 제5호

이 간행물의 다른 논문 (21건)

On Skew Centralizing Traces of Permuting n-Additive MappingsNazia Parveen, Mohammad Ashrafpp. 1-12Distributivity on the Gyrovector Spaces김세정pp. 13-20A Note on Skew-commuting Automorphisms in Prime RingsTarannum Bano, Nadeem Ur Rehmanpp. 21-28Functional Equations associated with Generalized Bernoulli Numbers and Polynomials장유선, 유천성, 권혁인, Dmitry Victorovich Dolgypp. 29-39Some Additive Maps on Sigma Prime RingsMohammad Mueenul Hasnain, Mohd Rais Khanpp. 41-50
원문 보기