This paper contains some new reverse dynamic inequalities of Hilbert-type on delta time scale calculus using mean inequality by applying reverse Hölder's inequality, chain rule on time scales, integration by parts, and the mean inequality. As special cases of our results, we get the discrete, continuous, and quantum analogs of inequalities, i.e., when $ \mathbb{T = N} $, $ \mathbb{T = R} $ and $ \mathbb{T = }q^{\mathbb{N}} $ for $ q > 1 $.
Citation: Elkhateeb S. Aly, Said Bourazza, Sultanah Masmali, Ahmed I. Saied. Some reverse dynamic inequalities of Hilbert-type using mean inequality[J]. AIMS Mathematics, 2026, 11(2): 4445-4464. doi: 10.3934/math.2026178
This paper contains some new reverse dynamic inequalities of Hilbert-type on delta time scale calculus using mean inequality by applying reverse Hölder's inequality, chain rule on time scales, integration by parts, and the mean inequality. As special cases of our results, we get the discrete, continuous, and quantum analogs of inequalities, i.e., when $ \mathbb{T = N} $, $ \mathbb{T = R} $ and $ \mathbb{T = }q^{\mathbb{N}} $ for $ q > 1 $.
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Elkhateeb S. Aly, Said Bourazza, Sultanah Masmali, Ahmed I. Saied. Some reverse dynamic inequalities of Hilbert-type using mean inequality[J]. AIMS Mathematics, 2026, 11(2): 4445-4464. doi: 10.3934/math.2026178
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