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APPROXIMATELY CONVEX SCHWARTZ DISTRIBUTIONS

정재영
한국수학교육학회|2009.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제16권 제2호|pp. 179-186

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참고문헌

키워드

convex functionconvex distributionϵ-convex functionsϵ-convex distributions.
주제분류수학

초록

Generalizing the approximately convex function which is introduced by D.H. Hyers and S.M. Ulam we establish an approximately convex Schwartz dis- tribution and prove that every approximately convex Schwartz distribution is an approximately convex function.

Abstract

Generalizing the approximately convex function which is introduced by D.H. Hyers and S.M. Ulam we establish an approximately convex Schwartz dis- tribution and prove that every approximately convex Schwartz distribution is an approximately convex function.

참고문헌 (10)

  1. S. Banach, "Theorie des Operationes Lineaires" (1932), Warsaw
  2. P. W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27, pp.76~86 (1984)
  3. E. Deeba, "On a class of functional equations in distribu-tions", J. Math. Anal. Appl, 223, pp.334~346 (1998)
  4. E. Deeba, "Distributional analog of a functional equation", Applied Math-ematics Letters, 16, pp.669~673 (2003)
  5. I. M. Gelfand, "Generalized functions IV" (1968), Academic. Press
  6. J. W. Green, "Approximately convex functions", Duke Math. J, 19, pp.499~504 (1952)
  7. L. Hormander, "The Analysis of Linear Partial Differential Operator I" (1983), Springer Verlag
  8. D. H. Hyers, "Approximately convex functions", Proc. Amer. Math. Soc, 3, pp.821~828 (1954)
  9. D. H. Hyers, "Stability of Functional Equations in Several Variables" (1998), Birkhauser
  10. L. Schwartz, "Theorie des distributions. I, II, 2nd ed" (1957), Hermann

관련 논문AI추천

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