본문 바로가기
KERD
논문KCI 등재

STABILITY OF TRIGONOMETRIC TYPE FUNCTIONAL EQUATIONS IN RESTRICTED DOMAINS

정재영
한국수학교육학회|2011.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제18권 제3호|pp. 231-244

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

exponential functionHyers-Ulam stabilityadditive functiontrigono-metric type functional equationheat kernel.
주제분류수학

초록

We prove the Hyers-Ulam stability for trigonometric type functional inequalities in restricted domains with time variables. As consequences of the result we obtain asymptotic behaviors of the inequalities and stability of related functional inequalities in almost everywhere sense.

Abstract

We prove the Hyers-Ulam stability for trigonometric type functional inequalities in restricted domains with time variables. As consequences of the result we obtain asymptotic behaviors of the inequalities and stability of related functional inequalities in almost everywhere sense.

참고문헌 (28)

  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 cosine functional equation", Proc. Amer. Math. Soc, 통권 : 80, pp.411~416 (1980)
  3. D.G. Bourgin, "Class of transformations and bordering transformations", Bull. Amer. Math. Soc, 57, pp.223~237 (1951)
  4. D.G. Bourgin, "Multiplicative transformations", Proc. Nat. Academy Sci. of U.S.A, 통권 : 36, pp.564~570 (1950)
  5. 정재영, "Stability of approximately quadratic Schwartz distributions", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 67, pp.175~186
  6. J. Chung, "A distributional version of functional equations and their stabilities", Nonlinear Analysis, 62, pp.1037~1051 (2005)
  7. Jeongwook Chang, "The stability of the sine and cosine functional equations in Schwartz distributions", 대한수학회보, 46(1), pp.87~97 (2009), 대한수학회
  8. S. Czerwik, "Stability of Functional Equations of Ulam-Hyers-Rassias Type" (2003), Hadronic Press, Inc
  9. G.L. Forti, "Hyer-Ulam stability of functional equation in several variables", Aequationes Math, 50, pp.143~190 (1995)
  10. D.H. Hyers, "On the stability of the linear functional equations", Proc. Nat. Acad. Sci. USA, 통권 : 27, pp.222~224 (1941)
  11. D.H. Hyers, "Stability of functional equations in several vari- ables" (1998), Birkhauser
  12. S.-M. Jung, "Hyers-Ulam stability of Jensen's equation and its application", Proc. Amer. Math. Soc, 통권 : 126, pp.3137~3143 (1998)
  13. K.-W. Jun, "Stability problem for Jensen-type functional equations of cubic mappings", Acta Mathematica Sinica, English Series, 22(6), pp.1781~1788 (2006)
  14. 이영환, "Boundedness of approximate trigonometric functions", APPLIED MATHEMATICS LETTERS, 22, pp.439~443
  15. C.G. Park, "Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algabras", Bull. Sci. Math, 132, pp.87~96 (2008)
  16. J.M. Rassias, "On the Ulam stability of Jensen and Jensen type mappings on restricted domains", J. Math. Anal. Appl, 281, pp.516~524 (2003)
  17. J.M. Rassias, "On the Ulam stability of mixed type mappings on restricted domains", J. Math. Anal. Appl, 276, pp.747~762 (2002)
  18. J.M. Rassias, "On Approximation of Approximately Linear Mappings by Linear Mappings", J. Funct. Anal, 46, pp.126~130 (1982)
  19. Th.M. Rassias, "On the stability of functional equations in Banach spaces", J. Math. Anal. Appl, 251, pp.264~284 (2000)
  20. Th.M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 통권 : 7, pp.297~300 (1978)
  21. K. Ravi, "On the Ulam-Gavruta-Rassias stability of the orthogonally Euler-Lagrange type functional equation", Intern. J. Appl. Math. Stat, 7, pp.143~156 (2007)
  22. F. Skof, "Sull'approssimazione delle applicazioni localmente γ-additive", Atii Accad. Sci.Torino Cl. Sci. Fis. Mat. Natur, 117, pp.377~389 (1983)
  23. L. Szekelyhidi, "The stability of sine and cosine functional equations", Proc. Amer. Math. Soc, 통권 : 110, pp.109~115 (1990)
  24. L. Szekelyhidi, "The stability of d'Alembert type functional equations", Acta Sci. Math. Szeged, 44, pp.313~320 (1982)
  25. I. Tyrala, "The stability of d'Alembert's functional equation", Aequationes Math, 69, pp.250~256 (2005)
  26. S.M. Ulam, "Problems in modern mathematics" (1960), Interscience Publ
  27. S.M. Ulam, "A Collection of Mathematical Problems. Science Editions" (1968), Wiley
  28. D.V. Widder, "The heat equation" (1975), Academic Press

관련 논문AI추천

Hyers-Ulam stability of trigonometric functional equations장정욱, 정재영대한수학회 · 대한수학회논문집2008 · 제23권 제4호ON THE STABILITY OF PEXIDER TYPE TRIGONOMETRIC FUNCTIONAL EQUATIONS김광휘강원경기수학회 · 한국수학논문집2008 · 제16권 제3호Stability of pexiderized Jensen and Jensen type functional equations on restricted domains최창권대한수학회 · 대한수학회보2019 · 제56권 제3호The stability of functional inequalities with additive mappingsKil-Woung Jun, Young-Sun Cho대한수학회 · 대한수학회보2009 · 제46권 제1호ASYMPTOTIC BEHAVIORS OF JENSEN TYPE FUNCTIONAL EQUATIONS IN HALF PLANES김규태, 김상엽, 박광현, 이기휘, 이재호한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제2호On the Superstability of the generalized Sine Functional Equations김광휘, 한미현강원경기수학회 · 한국수학논문집2011 · 제19권 제2호

이 간행물의 다른 논문 (8건)

A SIMPLE AUGMENTED JACOBI METHOD FOR HERMITIAN AND SKEW-HERMITIAN MATRICES이수준, 민조홍, 김세구pp. 185-199(DS)-WEAK COMMUTATIVITY CONDITION AND COMMON FIXED POINT IN INTUITIONISTIC MENGER SPACESSuresh Chouhan, Bhavana Deshpande, Sushil Sharmapp. 201-217ON THE RADIUS OF CONVERGENCE OF SOME NEWTON{TYPE METHODS IN BANACH SPACESIoannis K. Argyros, Said Hiloutpp. 219-230SUFFICIENT CONDITIONS FOR THE INTERSECTION PROPERTY IN GENERALIZED LI¶ENARD SYSTEMS김용인pp. 245-253SOME FIXED POINT THEOREM USING COMMON PROPERTY(E.A.) IN INTUITIONISTIC FUZZY METRIC SPACEJong Seo Parkpp. 255-260
원문 보기