Advanced simple and double integral inequalities with three-parameter ratio-minimum kernels

Document Type : Regular research papers

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University of Caen-Normandie

Abstract

Integral inequalities play a crucial role in various areas of mathematics, both in theoretical analysis and practical applications. The discovery of new forms of such inequalities remains an important and ongoing area of research. This article is a contribution in this sense. We present new integral inequalities involving three-parameter ratio-minimum weight functions or kernel functions. In particular, we establish simple integral inequalities of the weighted H\"older type and double integral inequalities of the Hardy-Hilbert type. The arctangent function plays a crucial role in defining the upper bounds. These results extend the classical inequalities by incorporating additional parameters, thereby increasing their flexibility and applicability. Detailed proofs are provided to ensure clarity and facilitate further research in this area.

The arctangent function plays a crucial role in defining the upper bounds. These results extend the classical inequalities by incorporating additional parameters, thereby increasing their flexibility and applicability. Detailed proofs are provided to ensure clarity and facilitate further research in this area.

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History

  • Receive Date: 24 April 2025
  • Revise Date: 09 May 2025
  • Accept Date: 01 August 2025

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