Rassias, Michael Th.; Yang, Bicheng Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function. (English) Zbl 1371.26036 Adv. Oper. Theory 2, No. 3, 237-256 (2017). Summary: By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardy-type integral inequalities with the homogeneous kernel are deduced. We also consider the operator expressions. Cited in 4 Documents MSC: 26D15 Inequalities for sums, series and integrals Keywords:Hardy-type integral inequality; weight function; equivalent form; Riemann zeta function; operator × Cite Format Result Cite Review PDF Full Text: DOI