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

: 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 H¨older’s inequalities on time scales. Our results encompass the continuous inequalities established by Benaissa as special cases when the time scale T corresponds to the real numbers (when T = R ). Additionally, we derive distinct inequalities within the realm of time scale calculus, such as cases T = N and q N for q > 1. These ﬁndings represent new and signiﬁcant contributions for the reader.

Here, we aim to extend the inequality (1.7) and rectify (1.8) in time scale calculus which is defined in Section 2. Also, we can get some new inequalities in (continuous, discrete, and quantum) calculus.For more information about dynamic inequalities, see for instance .

Preliminaries and basic lemmas
Theorem 2.1.[13] Let G, W : T → R be ∆-differentiable at τ ∈ T. Then we have the following at τ: (2) αG : T → R is differentiable for any constant α with (3) The product GW : T → R is differentiable and the product rule is defined by .
(5) If W(τ)W(σ(τ)) 0, then the quotient G/W : T → R is differentiable and the quotient rule is defined as In this case, the Cauchy integral of G is defined as Definition 2.2.
[13] A function f : T → R is called rd-continuous provided that it is continuous at right-dense points in T and its left-sided limits exist (finite) at left-dense points in T. The set of rd-continuous functions f : T → R is denoted by C rd (T, R).

Main results
During this study, we assume the existence of the integrals under consideration. Then, Proof.From (3.1), we see that Then, and Integrating (3.4) and (3.5) over ς from č to ȃ, we see that and .

Conclusions
In this paper, we have established a novel extensions of the reversed Minkowski's inequality for various functions on delta calculus time scales by applying Jensen's and Hölder's inequalities on time scales.In addition, we have presented some new inequalities in different cases, like T = N and q N for q > 1.
In the future, we will apply the reversed Minkowski inequality for various functions to diamondalpha calculus and conformable calculus time scales.

Use of AI tools declaration
The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.