Abstract
For the setM of convex-downward functions Ψ (•) vanishing at infinity, we present its decomposition into subsets with respect to the behavior of special characteristics η (Ψ;•) and μ(Ψ;•) of these functions. We study geometric and analytic properties of the elements of the subsets obtained, which are necessary for the investigation of problems of the theory of approximation for classes of convolutions.
Similar content being viewed by others
References
A. I. Stepanets, “The convergence rate of Fourier series on the classes of\(\bar \psi \),”Ukr. Mat. Zh.,49, No. 8, 1069–1113 (1997).
A. I. Stepanets,Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 5, pp. 688–702, May, 1999.
Rights and permissions
About this article
Cite this article
Stepanets, A.I. Several statements for convex functions. Ukr Math J 51, 764–780 (1999). https://doi.org/10.1007/BF02591710
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02591710