Novel generalized inequalities involving a general Hardy operator with multiple variables and general kernels on time scales

M. Zakarya; Ghada AlNemer; A. I. Saied; H. M. Rezk; M. Zakarya; Ghada AlNemer; A. I. Saied; H. M. Rezk

doi:10.3934/math.20241040

AIMS Mathematics

2024, Volume 9, Issue 8: 21414-21432. doi: 10.3934/math.20241040

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Novel generalized inequalities involving a general Hardy operator with multiple variables and general kernels on time scales

1.
King Khalid University, College of Science, Department of Mathematics, P.O. Box 9004, 61413 Abha, Saudi Arabia
2.
Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
3.
Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 04001, Košice, Slovakia
4.
Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt
5.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt

Received: 12 March 2024 Revised: 29 May 2024 Accepted: 06 June 2024 Published: 04 July 2024
MSC : 26D10, 26D15, 34N05, 42B25, 42C10, 47B38

This paper introduced novel multidimensional Hardy-type inequalities with general kernels on time scales, extending existing results in the literature. We established generalized inequalities involving a general Hardy operator with multiple variables and kernels on arbitrary time scales. Our findings not only encompassed known results in the realm of real numbers ($ \mathbb{T=R} $), but also provided refinements and generalizations thereof. The proposed inequalities offered versatile applications in mathematical analysis and beyond, contributing to the ongoing exploration of inequalities on diverse time scales.
- Hardy type inequality,
- Hardy's operator,
- weighted functions,
- inequalities with kernels,
- time scales
Citation: M. Zakarya, Ghada AlNemer, A. I. Saied, H. M. Rezk. Novel generalized inequalities involving a general Hardy operator with multiple variables and general kernels on time scales[J]. AIMS Mathematics, 2024, 9(8): 21414-21432. doi: 10.3934/math.20241040

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Abstract

This paper introduced novel multidimensional Hardy-type inequalities with general kernels on time scales, extending existing results in the literature. We established generalized inequalities involving a general Hardy operator with multiple variables and kernels on arbitrary time scales. Our findings not only encompassed known results in the realm of real numbers ($ \mathbb{T=R} $), but also provided refinements and generalizations thereof. The proposed inequalities offered versatile applications in mathematical analysis and beyond, contributing to the ongoing exploration of inequalities on diverse time scales.

References

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