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A Half-Discrete Hardy-Hilbert-Type Inequality with a Best Possible Constant Factor Related to the Hurwitz Zeta Function

In: Progress in Approximation Theory and Applicable Complex Analysis

Author

Listed:
  • Michael Th. Rassias

    (ETH-Zürich
    Princeton University)

  • Bicheng Yang

    (Guangdong University of Education)

Abstract

Using methods of weight functions, techniques of real analysis as well as the Hermite-Hadamard inequality, a half-discrete Hardy-Hilbert-type inequality with multi-parameters and a best possible constant factor related to the Hurwitz zeta function and the Riemann zeta function is obtained. Equivalent forms, normed operator expressions, their reverses and some particular cases are also considered.

Suggested Citation

  • Michael Th. Rassias & Bicheng Yang, 2017. "A Half-Discrete Hardy-Hilbert-Type Inequality with a Best Possible Constant Factor Related to the Hurwitz Zeta Function," Springer Optimization and Its Applications, in: Narendra Kumar Govil & Ram Mohapatra & Mohammed A. Qazi & Gerhard Schmeisser (ed.), Progress in Approximation Theory and Applicable Complex Analysis, pages 183-218, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-49242-1_10
    DOI: 10.1007/978-3-319-49242-1_10
    as

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