Some new generalizations of reversed Minkowski's inequality for several functions via time scales

Abstract

In this paper, we introduce novel extensions of the reversed Minkowski inequality for various functions defined on time scales. Our approach involves the application of Jensen's and Hölder's inequalities on time scales. Our results encompass the continuous inequalities established by Benaissa as special cases when the time scale $ \mathbb{T} $ corresponds to the real numbers (when $ \mathbb{T = R} $). Additionally, we derive distinct inequalities within the realm of time scale calculus, such as cases $ \mathbb{ T = N} $ and $ q^{\mathbb{N}} $ for $ q > 1 $. These findings represent new and significant contributions for the reader.

Keywords

• hölder's inequality
• inequalities on time scales
• jensen's inequality