This article is cited in 1 paper

Andreev–Korkin identity, Saigo fractional integration operator and $\mathrm{Lip}_L(\alpha)$ functions

D. Jankov^a, T. K. Pogány<sup>b

a</sup> Department of Mathematics, University of Osijek Trg Lj. Gaja 6, 31000 Osijek, Croatia
^b Faculty od Maritime Studies, University of Rijeka Studentska 2, 51000 Rijeka, Croatia

Abstract: The Andreev–Korkin identity for the Chebyshev functional is treated by Hölder inequality, when the functional consists of $\mathrm{Lip}_L(\alpha)$ functions. The derived upper bound is applied to the so-called Chebyshev–Saigo functional, built by Saigo fractional integral operator – recently introduced by Saxena et al. (R. K. Saxena, J. Ram, J. Daiya, and T. K. Pogány. – Integral Transforms Spec. Funct. 22 (2011), 671–680).

Key words and phrases: Chebyshev functional, Andreev–Korkin identity, Chebyshev–Saigo functional, Saigo hypergeometric fractional integration operator, Lipschitz function clas.

MSC: Primary 26D15, 26A16; Secondary 26A33, 26D10

Received: 26.10.2010
Revised: 25.05.2011

Language: English

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