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Some new inequalities for the gamma, beta and zeta functions. (English) Zbl 1182.33005
Summary: An inequality involving a positive linear operator acting on the composition of two continuous functions is presented. This inequality leads to new inequalities involving the beta, gamma and zeta functions and a large family of functions which are Mellin transforms.

MSC:
33B15 Gamma, beta and polygamma functions
26D07 Inequalities involving other types of functions
39B62 Functional inequalities, including subadditivity, convexity, etc.
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