Geodesic
Andreev–Korkin identity, Saigo fractional integration operator and $\mathrm{Lip}_L(\alpha)$ functions
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 2, pp. 144-157 
D. Jankov; T. K. Pogány. Andreev–Korkin identity, Saigo fractional integration operator and $\mathrm{Lip}_L(\alpha)$ functions. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 2, pp. 144-157. http://geodesic.mathdoc.fr/item/JMAG_2012_8_2_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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).

[1] D.S. Mitrinović and P.M. Vasić, “History, Variations and Generalisations of the Chebyshev Inequality and the Question of Some Priorities”, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 1974, no. 461–497, 1–30 | MR

[2] A.N. Korkin, “On a certain definite integral”, Mat. Sbornik, 10 (1884), 571–572 (Russian)

[3] A.N. Korkin, “Sur un théorème de M. Tchebychef”, C.R. Acad. Sci. Paris, 96 (1883), 326–327

[4] D.S. Mitrinović, J.E. Pečarić, and A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Acad. Publ., Dordrecht, 1993 | MR

[5] K.A. Andreev, “A few words on the theorems of P.L. Chebyshev and V.G. Imshenetskii about definite integrals of the product of functions”, Soobshcheniya i protokoli zasedaniy Matematicheskogo obshchestva pri Imperatorskom Khar'kovskom Universitete, 1883, 110–123 (Russian)

[6] A.M. Mathai, R.K. Saxena,and H.J. Haubold, The $H$-Function: Theory and Applications, Springer, New York, 2010 | MR

[7] B.C. Carlson, “Some Inequalities for Hypergeometric Functions”, Proc. Amer. Math. Soc., 17 (1966), 32–39 | DOI | MR | Zbl

[8] R.K. Saxena, J. Ram, J. Daiya, and T.K. Pogány, “Inequalities Associated with Chebyshev Functional for Saigo Fractional Integration Operator”, Integral Tranforms Spec. Funct., 22 (2011), 671–680 | DOI | MR | Zbl

[9] H.M. Srivastava, K.C. Gupta, and S.P. Goyal, The $H$-Functions of One and Two Variables with Applications, South Asian Publishers, New Delhi, 1982 | MR | Zbl