Some reverse Hölder inequalities with Specht's ratio on time scales

Abstract

In this article, we investigate some new reverse Hölder-type inequalities on an arbitrary time scale via the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals. These inequalities extend some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues.

Diamond alpha Bennett‐Leindler type dynamic inequalities and their applications

“…Then the aforementioned Hardy-Copson inequalities have been unified to an arbitrary time scale in the book 23 and in the papers [24][25][26][27][28][29][30][31] for the delta time scale calculus. In the delta time scale calculus, the reverse Hardy-Copson type inequalities, which are called delta Bennett-Leindler inequalities, can be found in previous works 28,[32][33][34] for 0 < q < 1. These results are unifications of discrete and continuous Bennett-Leindler inequalities mentioned above except the ones in Renaud.…”

Some dynamic inequalities on time scales and their applications

“…For more information and details on the time scales, we refer the reader to the books [22,23]. Many dynamic inequalities have been studied by different authors during the past decade (see [20,[24][25][26][27][28][29][30][31][32][33][34][35][36] and the references therein). Throughout this paper, the knowledge and understanding of the time scales and time scale notion are assumed.…”

A unified approach to fractal Hilbert-type inequalities

“…For some related extensions of classical inequalities to fractal spaces the reader is referred to recent papers [4-6, 9, 11-13, 16, 17]. In addition, for some recent results closely connected to this topic the reader is referred to [1,2,7,15] and the references therein.…”