A unified treatment of Hilbert–Pachpatte-type inequalities for a class of non-homogeneous kernels

摘要

In the present paper we establish a unified treatment of Hilbert–Pachpatte-type inequalities for a class of non-homogeneous kernels. Our results are derived in both discrete and integral versions. A particular emphasis is devoted to constants and weight functions appearing on the right-hand sides of the established inequalities. As an application, we obtain inequalities with constants and weight functions expressed in terms of generalized harmonic numbers, the incomplete Beta and Gamma function, and the logarithmic integral function.