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Статья
2019

One-parameter monotone functionals connected with Stieltjes integrals


F. G. AvkhadievF. G. Avkhadiev
Русская математика
https://doi.org/10.3103/S1066369X19040017
Abstract / Full Text

Using Stieltjes integrals we define one-parameter functionals that are monotone as a function on the parameter. We prove generalizations of some results from the papers:

  1. 1)

    Heinig H. and Maligranda L. Weighted inequalities for monotone and concave functions, Studia Math. 116 (2), 133–165 (1995)

  2. 2)

    Avkhadiev F.G. and Kayumov I.R. Comparison theorems of isoperimetric type for moments of compact sets, Collectanea Math. 55 (1), 1–9 (2004).

In contrast to these papers we prove several theorems on monotonicity of integral functionals in the case when integrating functions are not absolutely continuous. In addition, we obtain applications to isoperimetric inequalities.

Author information
  • Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008, RussiaF. G. Avkhadiev
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