Two new theorems on integral inequalities involving maximums and minimums of ratios

Christophe Chesneau

doi:10.14244/lajm.v5i1.64

Autores

Christophe Chesneau University of Caen-Normandie https://orcid.org/0000-0002-1522-9292

DOI:

https://doi.org/10.14244/lajm.v5i1.64

Palavras-chave:

Two-dimensional integral inequalities, Hardy-Hilbert-type integral inequalities, beta function, gamma function

Resumo

In this article, we present two new theorems relating to the upper bounds of specific two-dimensional integral inequalities. The first theorem uses certain maximums of the ratios of the two variables, while the second offers an analogous result based on certain minimums of these ratios. The obtained bounds are quite manageable, with constant factors defined by simple integrals. Complete proofs are provided for the sake of rigor. To illustrate the scope and implications of these results, we present several examples, some of which focus on the standard beta and gamma functions.

Biografia do Autor

Christophe Chesneau, University of Caen-Normandie

Department of Mathematics, LMNO

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