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APPROXIMATELY QUADRATIC DERIVATIONS AND GENERALIZED HOMOMORPHISMS

Park, Kyoo-Hong    (DEPARTMENT OF MATHEMATICS EDUCATION, SEOWON UNIVERSITY   ); Jung, Yong-Soo    (DEPARTMENT OF MATHEMATICS, SUN MOON UNIVERSITY  );
  • 초록

    Let $\cal{A}$ be a unital Banach algebra. If f : $\cal{A}{\rightarrow}\cal{A}$ is an approximately quadratic derivation in the sense of Hyers-Ulam-J.M. Rassias, then f : $\cal{A}{\rightarrow}\cal{A}$ is anexactly quadratic derivation. On the other hands, let $\cal{A}$ and $\cal{B}$ be Banach algebras.Any approximately generalized homomorphism f : $\cal{A}{\rightarrow}\cal{B}$ corresponding to Cauchy, Jensen functional equation can be estimated by a generalized homomorphism.


  • 주제어

    quadratic derivation .   approximate quadratic derivation .   stability.  

  • 참고문헌 (26)

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    19. Y.-S. Jung & I.-S. Chang: On approximately higher ring derivations. J. Math. Anal. Appl. 343 (2008), no. 2, 636-643. 
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    26. T. Miura, G. Hirasawa & S.-E. Takahasi: A perturbation of ring derivations on Banach algebras. J. Math. Anal. Appl. 319 (2006), 522-530. 

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    2. 1994 "Strong Higher Derivations on Ultraprime Banach Algebras" 충청수학회지 = Journal of the Chungcheong Mathematical Society 7 (1): 117~122    
    3. 1997 "ON THE SPECTRAL RADIUS AND INVERTIBILITY OF CERTAIN ELEMENTS IN BANACH ALGEBRA" Korean journal of computational & applied mathematics 4 (1): 299~308    
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    5. 1999 "FULL SPECTRUM PRESERVING LINEAR MAPPING BETWEEN STLICTLY DENSE BANACH ALGEBRAS" Korean journal of computational & applied mathematics 6 (1): 303~307    
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    8. 2000 "CONTINUOUS DERIVATIONS OF NONCOMMUTATIVE BANACH ALGEBRA" Korean journal of computational & applied mathematics 7 (1): 319~327    
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