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

Author

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  • Batbold, Tserendorj
  • Azar, Laith E.
  • Krnić, Mario

Abstract

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.

Suggested Citation

  • Batbold, Tserendorj & Azar, Laith E. & Krnić, Mario, 2019. "A unified treatment of Hilbert–Pachpatte-type inequalities for a class of non-homogeneous kernels," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 167-182.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:167-182
    DOI: 10.1016/j.amc.2018.09.047
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    References listed on IDEAS

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    1. Young-Ho Kim, 2001. "An improvement of some inequalities similar to Hilbert's inequality," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 28, pages 1-11, January.
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