On functional inequalities for the psi function

B. A. Bhayo^a, L. Xie^b, Ş. Yildiz Yar<sup>c

a</sup> School of Energy Systems Lappeenranta-Lahti University of Technology, 15210 Lahti, Finland
^b School of Energy & Environmental Engineering, Hebei University of Technology, Tianjin, 300401, China
^c Department of Mathematics, Ordu University, Cumhuriyet Campus, Turkey

Abstract: Motivated by the works of Bougotta and Mercer, the authors in this paper study the monotonicity of the function $x\mapsto\psi(1+bx)^a/\psi(1+ax)^b$, and establish several inequalities involving the psi function.

Keywords: gamma function, polygamma function, inequalities.

UDC: 517.58

MSC: 33B15, 26D15

Received: 10.12.2024
Revised: 11.05.2025
Accepted: 11.05.2025

Language: English

DOI: 10.15393/j3.art.2025.17250