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2018•Proceedings of the American Mathematical SocietyOpen access

A class of completely mixed monotonic functions involving the gamma function with applications

Zhen-Hang Yang, Jing-Feng Tian

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Abstract

In this paper, we introduce the notion of completely mixed monotonicity of a function of several variables, very few of which have appeared. We give a necessary and sufficient condition for a function constructed by ratios of gamma functions to be completely mixed monotonic. From this, some new inequalities for gamma, psi, and polygamma functions are derived.

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What this paper is about

In this paper, we introduce the notion of completely mixed monotonicity of a function of several variables, very few of which have appeared. We give a necessary and sufficient condition for a function constructed by ratios of gamma functions to be completely mixed monotonic. From this, some new inequalities for gamma, psi, and polygamma functions are derived.

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OpenAlex reports 40 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we introduce the notion of completely mixed monotonicity of a function of several variables, very few of which have appeared. We give a necessary and sufficient condition for a function constructed by ratios of gamma functions to be completely mixed monotonic. From this, some new inequalities for gamma, psi, and polygamma functions are derived.

Key concepts: Monotonic function, Gamma function, Mathematics, Class (philosophy), Function (biology), Pure mathematics, Applied mathematics, Mathematical analysis

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