Analysis Mathematica

, Volume 43, Issue 3, pp 501–510 | Cite as

On the smoothness of certain composite functions

  • P. V. ManhEmail author


We give a characterization of the class R d m of all functions f for which the composite function xf(\(\sqrt[m]{x}\) ) is d-times continuously differentiable in [0, 1]. Some properties of R d m are also investigated.

Key words and phrases

composite function smoothness of composite function 

Mathematics Subject Classification

primary 26A24 26A27 


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  1. [1]
    B. Bojanov, H. A. Hakopian and A. Sahakian, Spline functions and multivariate interpolations, Springer-Verlag (berlin, 1993).CrossRefzbMATHGoogle Scholar
  2. [2]
    L. H. Encinas and J. M. Masque, A short proof of the generalized Faà di Bruno’s formula, Appl. Math. Lett., 16 (2003), 975–979.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    L. Filipsson, Complex mean-value interpolation and approximation of holomorphic functions, J. Approx. Theory, 91 (1997), 244–278.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    S. Roman, The formula of Faà di Bruno, Amer. Math. Monthly, 87 (1980), 805–809.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach (Amsterdam, 1993).zbMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationCaugiay, HanoiVietnam

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