Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 493, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2020.124478
Keywords
Inequality; Exponential function; Sum; Logarithmically complete monotonicity; Ratio; Gamma function
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The authors of this paper review a series of inequalities involving finitely many exponential functions and sums, establishing new inequalities, exploring properties of ratios of finitely many gamma functions, and investigating monotonicity and concavity of related functions.
In this paper, the authors review origins, motivations, and generalizations of a series of inequalities involving finitely many exponential functions and sums. They establish three new inequalities involving finitely many exponential functions and sums by finding convexity of a function related to the generating function of the Bernoulli numbers. They also survey the history, backgrounds, generalizations, logarithmically complete monotonicity, and applications of a series of ratios of finitely many gamma functions, present complete monotonicity of a linear combination of finitely many trigamma functions, construct a new ratio of finitely many gamma functions, derive monotonicity, logarithmic convexity, concavity, complete monotonicity, and the Bernstein function property of the newly constructed ratio of finitely many gamma functions. Finally, they suggest two linear combinations of finitely many trigamma functions and two ratios of finitely many gamma functions to be investigated. (c) 2020 Elsevier Inc. All rights reserved.
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