Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios

In the paper, with the aid of the Cebysev integral inequality, by virtue of the integral representation of the Riemann zeta function, with the use of two properties of a function and its derivatives involving the exponential function and the Stirling numbers of the second kind, by means of complete monotonicity, the authors establish logarithmic convexity and increasing property of four sequences involving the Bernoulli numbers and their ratios.

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