| Summary: | In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-<inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">T</mi><mo>=</mo><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>.
|
|---|