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More accurate dynamic Hardy-type inequalities obtained via superquadraticity

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Utilizing the concept of a superquadratic function, in the present paper we establish some general weighted Hardy-type inequalities involving dynamic integral operators with a non-negative kernel. Our general results are then applied to some particular one-dimensional cases to provide refinements of some Hardy-type inequalities on time scales, known from the literature. In particular, we show that our results may be seen as generalizations of some recent results closely connected to classical one-dimensional Hardy’s, Pó lya-Knopp’s and Hardy-Hilbert’s inequalities on time scales.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Samir H. Saker

  2. Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, 11884, Egypt

    Haytham M. Rezk

  3. University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, 10000, Zagreb, Croatia

    Mario Krnić

Authors
  1. Samir H. Saker
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  2. Haytham M. Rezk
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  3. Mario Krnić
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Correspondence to Mario Krnić.

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Saker, S.H., Rezk, H.M. & Krnić, M. More accurate dynamic Hardy-type inequalities obtained via superquadraticity. RACSAM 113, 2691–2713 (2019). https://doi.org/10.1007/s13398-019-00654-z

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