This study explores a new reverse multidimensional Hilbert-type inequality with one partial sum (for \(p<0\) ), by utilizing transfer formula and Hermite–Hadamard’s inequality. The kernel \(\frac{1}{\left( u(n)+\left\| v(k)\right\| _{\alpha }\right) ^{\lambda +m}}(\lambda >0)\) in the new inequality has two general intermediate variables compared with previous work, and the best value is achieved with certain parameters. Finally, the equivalent forms and some particular cases are presented.

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A New Reverse Multidimensional Hilbert-Type Inequality with One Partial Sum

  • Michael Th. Rassias,
  • Bicheng Yang

摘要

This study explores a new reverse multidimensional Hilbert-type inequality with one partial sum (for \(p<0\) ), by utilizing transfer formula and Hermite–Hadamard’s inequality. The kernel \(\frac{1}{\left( u(n)+\left\| v(k)\right\| _{\alpha }\right) ^{\lambda +m}}(\lambda >0)\) in the new inequality has two general intermediate variables compared with previous work, and the best value is achieved with certain parameters. Finally, the equivalent forms and some particular cases are presented.