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Approximation of Cauchy additive mappings

노재옥|Hui Joung Shin
대한수학회 (The Korean Mathematical Society)|2007.11|대한수학회보 (Bulletin of the KMS)|제44권 제4호|pp. 851-859

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Abstract

In this paper, we prove that a function satisfying the follow-ing inequalityk f(x) + 2 f(y) + 2 f(z) k k 2f(x2+ y + z) k + (k x kr ky kr kz kr)for all x;y;z2 X and for 0, is Cauchy additive. Moreover, we willinvestigate for the stability in Banach spaces.

참고문헌 (12)

  1. "On stability of additive mappings" (1991)
  2. "On the stability of the linear functional equation" (1941)
  3. "Stability of functional equations in sev-eral variables Progress in Nonlinear Dierential Equations and their Applications" (1998), 34. Birkhauser Boston, Inc., Boston, MA
  4. "A generalization of the Hyers-Ulam-Rassias stability of the Pexider-ized quadratic equations", 297(1), pp.70~86 (2004)
  5. "Hyers-Ulam-Rassias stability of functional equations in mathematical analysis" (2001), Hadronic Press, Inc., Palm Harbor, FL
  6. "Homomorphisms between Poisson JC-algebras", (N.S.)36(1), pp.79~97 (2005)
  7. "Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras"
  8. "Functional inequalities associated with Jordan-vonNeumann-type additive functional equations", pp.113~ (2007)
  9. "On approximation of approximately linear mappings by linear mappings" (1982)
  10. "On the stability of the linear mapping in Banach spaces" (1978)
  11. "On the behavior of mappings which do not satisfy Hyers-Ulam stability" (1992)
  12. "A collection of mathematical problems Interscience Tracts in Pure andApplied Mathematics", 8 Interscience Publishers

관련 논문AI추천

Generalized Jensen's Functional Equations and Approximate Algebra Homomorphisms박원길, 배재형대한수학회 · 대한수학회보2002 · 제39권 제3호On the Hyers-Ulam stability of a generalized quadratic and additive functional equation김학만, 전길웅대한수학회 · 대한수학회보2005 · 제42권 제1호ON THE STABILITY OF A GENERALIZED ADDITIVE FUNCTIONAL EQUATION II신동윤, 이정례, 이태극한국수학교육학회 · 이론수학과 교직수학2007 · 제14권 제2호The nearly additive mapsEsmaeeil Ansari-Piri, Nasrin Eghbali대한수학회 · 대한수학회보2009 · 제46권 제2호On the Hyers-Ulam-Rassias stability of a modified additive and quadratic functional equation김학만, 전길웅, Don O Lee한국수학교육학회 · 이론수학과 교직수학2004 · 제11권 제4호On the Stability of the generalized $G$-type functional equationsGwang Hui Kim대한수학회 · 대한수학회논문집2005 · 제20권 제1호

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