Inequalities for Basic Special Functions Using Hölder Inequality

Mohammad Masjed-Jamei (), Zahra Moalemi and Nasser Saad
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Mohammad Masjed-Jamei: Department of Mathematics, K. N. Toosi University of Technology, Tehran P.O. Box 16315-1618, Iran
Zahra Moalemi: Department of Mathematics, K. N. Toosi University of Technology, Tehran P.O. Box 16315-1618, Iran
Nasser Saad: School of Mathematical and Computational Sciences, University of Prince Edward Island, Charlottetown, PE C1A 4P3, Canada

Mathematics, 2024, vol. 12, issue 19, 1-14

Abstract: Let p , q ≥ 1 be two real numbers such that 1 p + 1 q = 1 , and let a , b ∈ R be two parameters defined on the domain of a function, for example, f . Based on the well known Hölder inequality, we propose a generic inequality of the form | f ( a p + b q ) | ≤ | f ( a ) | 1 p | f ( b ) | 1 q , and show that many basic special functions, such as the gamma and polygamma functions, Riemann zeta function, beta function and Gauss and confluent hypergeometric functions, satisfy this type of inequality. In this sense, we also present some particular inequalities for the Gauss and confluent hypergeometric functions to confirm the main obtained inequalities.

Keywords: Hölder inequality; gamma and beta functions; Gauss and confluent hypergeometric functions; Riemann zeta function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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