On the asymptotic behaviour of pexiderized additive mapping on semigroups

• Autorzy: Alimohammady M , Sadeghi A
• Języki publikacji: EN

Abstrakty

EN

In this paper some asymptotic behaviors of the Pexiderized additive mappings can be proved for functions on commutative semigroup to a complex normed linear space under some suitable conditions. As a consequence of our result, we give some generalizations of Skof theorem and S.-M. Joung theorem. Furthermore, in this note we present a affirmative answer to problem 18, in the thirty-first ISFE.

Słowa kluczowe

EN

asymptotic behavior; stability; additive mappings; Pexiderized additive mapping

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2012
• Tom: Nr 49
• Strony: 5--14
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Alimohammady M

• Department of Mathematics University of Mazandaran Babolsar, Iran

autor

Sadeghi A

• Department of Mathematics University of Mazandaran Babolsar, Iran

Bibliografia

• [1] Alexander R., Blair C.-E., Rubel L.-A., Approximate version of Cauchy’s functional equation, Illinois J. Math., 39(1995), 278-287.
• [2] Alimohammady M., Sadeghi A., On the superstability of the Pexider type of exponential equation in Banach algebra, Int. J. Nonlinear Anal. Appl., (2011)(m press).
• [3] Alimohammady M., Sadeghi A., Some new results on the superstablity of the Cauchy equation on semigroup, Results Math., (2012)(m press).
• [4] Aoki T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2(1950), 64-66.
• [5] Baker J.A., A general functional equation and its stability, Proc. Amer. Math. Soc., 133(2005), 1657-1664.
• [6] Baker J.A., The stability of the cosine equation, Proc. Amer. Math. Soc., 80(1980), 411-416.
• [7] Czerwik S., On the stability of the homogeneous mapping, G. R. Math. Rep. Acad. Sci. Canada XIV, 6(1992), 268-272.
• [8] Elliott P.-D.-T.-A., Cauchy’s functional equation in the mean, Advances in Math., 51(1984), 253-257.
• [9] Forti G.-L., Hyers-Ulam stability of functional equations in several variables, Aeq. Math., 50(1995), 143-190.
• [10] Forti G.-L., Remark 11 in: Report of the 22nd Internat. Symposium on Functional Equations, Aequationes Math., 29(1980), (1985), 90-91.
• [11] Ger R., Šemrl P., The stability of the exponential equation, Proc. Amer. Math. Soc., 124(1996), 779-787.
• [12] Hyers D.-H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27(1941), 222-224.
• [13] Hyers D.-H., Isac G., Rassias Th.-M., On the asymptoticity aspect of Hyers-Ulam stability of mappings, Proc. Amer. Math. Soc., 126(2)(1998), 425-430.
• [14] Hyers D.-H., Rassias Th.-M., Approximate homomorphisms, Aeq. Math., 44(1992), 125-153.
• [15] Hyers D.-H., The stability of homomorphisms and related topics, in Global Analysis-Analysis on manifolds (ed. Th. M Rassias), Teubner-Texte zur Math., Leipzig, 57(1983), 140-153.
• [16] Hyers D.-H., Ulam S.-M., Approximately convex functions, Proc. Amer. Math. Soc., 3(1952), 821-828.
• [17] Hyers D.-H., Isac G., Rassias Th.-M., Stability of Functional Equations in Several Variables, Birkhauser, Boston,Basel, Berlin (1998).
• [18] Isac G.-Th.-M., Rassias Th.-M., Stability of ᴪ-additive mappings: Applications to nonlinear analysis, Internat. J. Math. & Math. Sci., 19(2)(1996), 219-228.
• [19] Jarosz K., Almost multiplicative functionals, Studia Math., 124(1997), 37-58.
• [20] Joung S.M., Hyers-Ulam-Rassias stability of Jensen’s equation and its apli- cations, Proc. Amer. Math. Soc., 126(1998), 3137-3143.
• [21] Kannappan Pl., Functional Equations and Inequalities with Applications, Springer, New York, 2009.
• [22] Nikodem K., Approximately quasiconvex functions, C. R. Math. Rep. Acad. Sci. Canada, 10(1988), 291-294.
• [23] Johnson B.-E., Approximately multiplicative functionals, J. London Math. Soc., 34(2)(1986), 489-510.
• [24] Jung S.-M., Superstability of homogeneous functional equation, Kyungpook Math. J., 38(1998), 251-257.
• [25] Jung S.-M., Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer, New York, 2011.
• [26] Rassias Th.-M., On the stability of functional equations and a problem of Ulam, Acta Applicandae Mathematicae, 62(2000), 23-130.
• [27] Rassias Th.-M., Problem 18, In: Report on the 31st ISFE, Aequationes Math., 47(1994), 312-13.
• [28] Rassias Th.-M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc, 72(1978), 297-300.
• [29] Rassias Th.-M., The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl., 246(2000), 352-378.
• [30] Rassias Th.-M., Brzdek j., (eds.), Functional Equations in Mathematical Analysis, Springer, New York, 2012.
• [31] Skof F., Propriety locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano, 53(1983), 113-129.
• [32] Tabor J., Tabor j., Homogenity is superstable, Publ. Math. Debrecen, 45 (1994), 123-130.
• [33] Ulam S.M., Problems in Modern Mathematics, Science Editions, Wiley, New York, 1960.