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On the improvements of Hardy and Copson inequalities

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

Abstract

In this current work, we revisit the recent improvements of the discrete Hardy’s inequality in one dimension and establish an extended improved discrete Hardy’s inequality with its optimality. We also study one-dimensional discrete Copson’s inequality (Copson in J. Lond. Math. Soc. 1–2(1):9–12, 1927), and achieve an improvement of the same in a particular case. Further, we study some fundamental structures such as completeness, Köthe–Toeplitz duality, separability, etc. of the sequence spaces which originated from the improved discrete Hardy and Copson inequalities in one dimension.

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Acknowledgements

The authors are thankful to the anonymous Reviewer for his/her reviews and valuable comments & suggestions that helped us to improve the manuscript. The authors are also very much thankful to Prof. David Krejčiřík (Prague, Czech Republic) for his valuable comments on the first draft of our manuscript.

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Authors and Affiliations

  1. Dr. APJ Abdul Kalam Technical University, Lucknow, 226021, India

    Bikram Das

  2. Indian Institute of Carpet Technology, Chauri Road, Bhadohi, Uttar Pradesh, 221401, India

    Bikram Das & Atanu Manna

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  1. Bikram Das
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  2. Atanu Manna
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Correspondence to Atanu Manna.

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Das, B., Manna, A. On the improvements of Hardy and Copson inequalities. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 92 (2023). https://doi.org/10.1007/s13398-023-01426-6

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