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<p>We establish new results for ◊<sub>∝</sub>-inequalities on time scales and formulate some dynamic Hilbert-type inequalities on the ◊<sub>∝</sub>-calculus of time scales for functions ◊<sub>∝</sub>-differentiable with respect to one and two variables. We obtain discrete and continuous inequalities as exceptional cases of our results (𝕋 = ℤ, 𝕋 = ℝ, and 𝕋 = <i>k</i>ℤ, where <i>k</i> &gt; 0). In addition, we can derive some other inequalities on different time scales, such as 𝕋 = <i>q</i><sup>ℤ</sup>, where <i>q</i> &gt; 1. These inequalities are proved by using Hölder’s inequality and the mean inequality.</p>

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New Developments of Dynamic Inequalities on Time Scales

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Lütfi Akin,
  • Hilal Orhan

摘要

We establish new results for ◊∝-inequalities on time scales and formulate some dynamic Hilbert-type inequalities on the ◊∝-calculus of time scales for functions ◊∝-differentiable with respect to one and two variables. We obtain discrete and continuous inequalities as exceptional cases of our results (𝕋 = ℤ, 𝕋 = ℝ, and 𝕋 = kℤ, where k > 0). In addition, we can derive some other inequalities on different time scales, such as 𝕋 = qℤ, where q > 1. These inequalities are proved by using Hölder’s inequality and the mean inequality.