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A new upper bound in the second Kershaw's double inequality and its generalizations |
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| Authors: | Feng Qi Senlin Guo Shou-Xin Chen |
| Institution: | aCollege of Mathematics and Information Science, Henan University, Kaifeng City, Henan Province 475001, China;bResearch Institute of Mathematical Inequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China;cDepartment of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2 |
| Abstract: | In the paper, a new upper bound in the second Kershaw's double inequality involving ratio of gamma functions is established, and, as generalizations of the second Kershaw's double inequality, the divided differences of the psi and polygamma functions are bounded. |
| Keywords: | Kershaw's double inequality Ratio of gamma functions Psi function Polygamma function Divided difference Upper bound Refinement Extension Generalization Identric mean Exponential mean Generalized logarithmic mean Completely monotonic function Logarithmically completely monotonic function |
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