Monotonicity Results For The Gamma Function

The function 1/x x+1 is strictly decreasing on[1,∞), the function [Γ(x+1)]1/x √ x is strictly increasing on[2,∞), and the function 1/x √ x+1 is strictly increasing on[1,∞), respectively. From these, some inequalities, for example, the Minc-Sathre inequality, are deduced, and two open problems posed by the second author are solved partially.

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