Unveiling new reverse Hilbert-type dynamic inequalities within the framework of Delta calculus on time scales

Haytham M. Rezk; Mohammed Zakarya; Amirah Ayidh I Al-Thaqfan; Maha Ali; Belal A. Glalah; Haytham M. Rezk; Mohammed Zakarya; Amirah Ayidh I Al-Thaqfan; Maha Ali; Belal A. Glalah

doi:10.3934/math.2025104

AIMS Mathematics

2025, Volume 10, Issue 2: 2254-2276. doi: 10.3934/math.2025104

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Unveiling new reverse Hilbert-type dynamic inequalities within the framework of Delta calculus on time scales

1.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt
2.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
3.
Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Sarat Ubaidah, Saudi Arabia
4.
Department of Basic Science, Higher Technological Institute, Sixth of October, October 12573, Egypt

Received: 31 August 2024 Revised: 05 January 2025 Accepted: 10 January 2025 Published: 08 February 2025
MSC : 26D10, 26D15, 42B25, 42C10, 47B38

Some new reverse versions of Hilbert-type inequalities are studied in this paper. The results are established by applying the time scale versions of reverse Hölder's inequality, reverse Jensen's inequality, chain rule on time scales, and the mean inequality. As applications, some particular results (when $ \mathbb{T = N} $ and $ \mathbb{T = R} $) are considered. Our results provide some new estimates for these types of inequalities and improve some of those recently published in the literature.
- Hilbert-type inequalities,
- reverse Hilbert-type inequality,
- delta calculus,
- time scales
Citation: Haytham M. Rezk, Mohammed Zakarya, Amirah Ayidh I Al-Thaqfan, Maha Ali, Belal A. Glalah. Unveiling new reverse Hilbert-type dynamic inequalities within the framework of Delta calculus on time scales[J]. AIMS Mathematics, 2025, 10(2): 2254-2276. doi: 10.3934/math.2025104

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Abstract

Some new reverse versions of Hilbert-type inequalities are studied in this paper. The results are established by applying the time scale versions of reverse Hölder's inequality, reverse Jensen's inequality, chain rule on time scales, and the mean inequality. As applications, some particular results (when $ \mathbb{T = N} $ and $ \mathbb{T = R} $) are considered. Our results provide some new estimates for these types of inequalities and improve some of those recently published in the literature.

References

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