M. Bouali

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math.GM2024

Convexity and concavity of a class of functions related to the elliptic functions

Mohamed Bouali

We investigate the convexity property on $(0, 1)$ of the function $f_{a} (x) = \frac{K ( x )}{a - ( 1/2 ) lo g ( 1 - x )} .$ We show that $f_{a}$ is strictly convex on $(0, 1)$ if and on…

math.GM2024

A mean value inequalities for the polygamma and zeta functions

Mohamed Bouali

A recently published result states inequalities of the harmonic mean of the digamma function. In this work, we prove among others results that for all positive real numbers $x\neq…

math.GM2024

Convexity properties related to Gauss hypergeometric function

Mohamed Bouali

We investigate the convexity property on $(0, 1)$ of the functions $φ_{a, b, c}$ and $1/ φ_{a, b, c}$ , where $φ_{a, b, c} (x) = \frac{c - lo g ( 1 - x )}{_{2} F _{1} ( a , b , a + b , x )},$ whenever $a,b\geq 0…