논문KCI 등재
A Fixed Point Approach to the Stability of a Functional Equation
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
By using an idea of Cadariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y, z - w) + f(x - y, z + w) = 2f(x, z) + 2f(y,w). The quadratic form f : R × R → R given by f(x, y) = ax² + by² is a solution of the above functional equation.
Abstract
By using an idea of Cadariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y, z - w) + f(x - y, z + w) = 2f(x, z) + 2f(y,w). The quadratic form f : R × R → R given by f(x, y) = ax² + by² is a solution of the above functional equation.
참고문헌 (13)
- J. H. Bae, "On stability of a functional equation with n variables", Nonlinear Anal. TMA, 64, pp.856~868 (2006)
- J. H. Bae, "On a cubic equation and a Jensen-quadratic equation", Abstarct Appl. Anal., 2007 (2007)
- J. H. Bae, "A fixed point approach to the stability of a functional equation on quadratic forms, preprint", ~
- L. Cădariu, "Fixed points and the stability of Jensen's functional equation", J. Inequal. Pure Appl. Math., 4 (2003)
- P. Găvruta, "A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings", J. Math. Anal. Appl., 184, pp.431~436 (1994)
- D. H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U. S. A., 27, pp.222~224 (1941)
- B. Margolis, "A fixed point theorem of the alternative for contractions on a generalized complete metric space", Bull. Amer. Math. Soc., 126, pp.305~309 (1968)
- W. G. Park, "On a Cauchy-Jensen functional equation and its stability", J. Math. Anal. Appl., 323, pp.634~643 (2006)
- W. G. Park, "A multidimensional functional equation having quadratic forms as solutions", J. Inequal. Appl., 2007 (2007)
- Won-Gil Park, "A Functional Equation Related to Quadratic Forms without the Cross Product Terms", 호남수학학술지, 30(2), pp.219~225 (2008), 호남수학회
- W. G. Park, "A functional equation originating from elliptic curves", Appl. Anal., 2008 (2008)
- Th. M. Rassias, "On the stability of linear mappings in Banach spaces", Proc. Amer. Math. Soc., 72, pp.297~300 (1978)
- S. M. Ulam, "A Collection of Mathematical Problems" (1968), Interscience Publishers
관련 논문AI추천
A Fixed Point Approach to the Stability of a Generalized Quadratic and Additive Functional Equation이양희, 진선숙경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제2호A FIXED POINT APPROACH TO THE STABILITY OF THE QUADRATIC-ADDITIVE FUNCTIONAL EQUATION박원길, 배재형, 이양희, 진선숙한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제4호A FIXED POINT APPROACH TO THE STABILITY OF A QUADRATIC-CUBIC-QUARTIC FUNCTIONAL EQUATION이양희영남수학회 · East Asian Mathematical Journal2019 · 제35권 제5호A fixed point approach to the stability of a quadratic-cubic functional equation이양희강원경기수학회 · 한국수학논문집2019 · 제27권 제2호On the Stability of a Quadratic Functional EquationJae-Hyeong Bae, Kil-Woung Jun, Soon-Mo Jung경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제3호A Fixed Point Approach to the Stability of an Additive-cubic-quartic Functional Equation이양희한국수학교육학회 · 이론수학과 교직수학2019 · 제26권 제4호
이 간행물의 다른 논문 (9건)
On a Structure Defined by a Tensor Field F of Type (1, 1) Satisfying Πj=1k [F2 + a(j)F + λ2(j)I] = 0Abhishek Singh, Lovejoy Das, Ram Nivaspp. 455-463Extreme Preservers of Zero-term Rank Sum over Fuzzy MatricesYeon-Jung Na, 송석준pp. 465-472On a q-Extension of the Leibniz Rule via Weyl Type of q-Derivative OperatorSunil Dutt Purohitpp. 473-482Dynamics of Recursive Sequence of Order TwoElsayed Mohammed Elsayedpp. 483-497Univalent Holomorphic Functions with Negative and Fixed Finitely Many Coefficients in terms of Generalized Fractional DerivativeShahram Najafzadeh, Rasoul Aghalary, Ali Ebadianpp. 499-507