In this paper, we establish sufficient conditions for Qi type diamond-alpha integral inequalities and its generalized form on time scales.

The theory of the calculus of variations was recently extended to the more general time scales setting, both for delta and nabla integrals. The primary purpose of this paper is to further extend the theory on time scales, by establishing some basic diamond-alpha dynamic integral inequalities. We prove generalized versions of Hölder, Cauchy-Schwarz, Minkowski, and Jensen’s inequalities. For the ...

In this paper, we introduce the concept of n-dimensional Diamond-Alpha integral on time scales. particular, it transforms into multiple Delta, Nabla and mixed integrals by taking different values alpha. Some its properties are explored, relationship between is provided. As an application, establish some weighted Ostrowski type inequalities through new integral. These expand known in monographs ...

In this paper, we aim to construct $n$ dimensional Jensen, Hardy and Hermite-Hadamard type inequalities for multiple diamond-alpha integral on time scales. The cases of inequality with a weighted function three variables are also considered minutely.

Abstract We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. first give definition and some properties interval integral that are naturally investigated as an extension nabla delta integrals. With help integral, we present variants Jensen inequalities convex concave functions on arbitrary scale. Moreover, Hölder’s Minkowski’s proved. Also, severa...

In this article, we give a new version of n-tuple diamond-alpha H¨older inequality on time scales, result generalizes some results known in the literature. Second, present with two parameters scales. It is tool to generalize integral inequalities its goal create an restarted from left side parameter right parameters. Moreover, Minkowski given, and interesting are found.