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STABILITY OF A FUNCTIONAL EQUATION IN COMPLEX BANACH SPACES

Yıl 2016, Cilt: 6 Sayı: 2, 307 - 314, 01.12.2016

Öz

Using fixed point technique, in the present paper , we wish to examine generalization of the Hyers-Ulam-Rassias stability theorem for the functional equations f 2 x + i y + f x + 2 i y = 4 f x + i y + f x + f y 0.1 and f 2 x + i y − f i x − 2 y = − 4 f i x − y + f x − f − y 0.2 in complex Banach spaces .

Kaynakça

  • Czerwik,S., (1992) On the stability of the quadratic mappings in normed spaces, Abh. Math. Sem. Univ. Hamburg,62, pp. 59-64.
  • Chang,I.S. and Kim,H.M., (2002), On the Hyers-Ulam stability of quadratic functional equations, J. Ineq. Pure App. Math. 3 No. 3 Art. 33, pp. 1-12.
  • Forti,G.L., (1995), Hyers-Ulam stability of functional equations in several variables, Aeq. Math., 50, pp. 143-190.
  • Gavruta,P., (1982), A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Func. Anal., 46, pp. 126-130.
  • Hyers,D.H., (1941), On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27, pp. 222-224.
  • Jun,K.W., Kim,H.M. and Lee,D.O., (2002), On the stability of a quadratic functional equation, J. Chung. Math. Sci., volume 15, no.2, pp. 73-84.
  • Jun,K.W., Shin,D.S. and Kim,B.D., (1999), On Hyers-Ulam-Rassias stability of the Pexider equation, J. Math. Anal. Appl. 239, pp. 20-29.
  • Jung,S.M., (1999), On the Hyers-Ulam-Rassias stability of a quadratic functional equations, J. Math. Anal. Appl. 232, pp. 384-393.
  • Rassias,T.M., (1978), On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72, pp. 297-300.
  • Ulam,S.M., (1960), Problems in Modern Mathematics, Cahp. VI, Wiley, New York.
  • Diaz,J. and Margolis,B., (1968), A fixed point theorem of alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74, pp. 305-309.
Yıl 2016, Cilt: 6 Sayı: 2, 307 - 314, 01.12.2016

Öz

Kaynakça

  • Czerwik,S., (1992) On the stability of the quadratic mappings in normed spaces, Abh. Math. Sem. Univ. Hamburg,62, pp. 59-64.
  • Chang,I.S. and Kim,H.M., (2002), On the Hyers-Ulam stability of quadratic functional equations, J. Ineq. Pure App. Math. 3 No. 3 Art. 33, pp. 1-12.
  • Forti,G.L., (1995), Hyers-Ulam stability of functional equations in several variables, Aeq. Math., 50, pp. 143-190.
  • Gavruta,P., (1982), A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Func. Anal., 46, pp. 126-130.
  • Hyers,D.H., (1941), On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27, pp. 222-224.
  • Jun,K.W., Kim,H.M. and Lee,D.O., (2002), On the stability of a quadratic functional equation, J. Chung. Math. Sci., volume 15, no.2, pp. 73-84.
  • Jun,K.W., Shin,D.S. and Kim,B.D., (1999), On Hyers-Ulam-Rassias stability of the Pexider equation, J. Math. Anal. Appl. 239, pp. 20-29.
  • Jung,S.M., (1999), On the Hyers-Ulam-Rassias stability of a quadratic functional equations, J. Math. Anal. Appl. 232, pp. 384-393.
  • Rassias,T.M., (1978), On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72, pp. 297-300.
  • Ulam,S.M., (1960), Problems in Modern Mathematics, Cahp. VI, Wiley, New York.
  • Diaz,J. and Margolis,B., (1968), A fixed point theorem of alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74, pp. 305-309.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Pratap Mondal Bu kişi benim

T. K. Samanta Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 2

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