New Hilbert dynamic inequalities on time scales

Abstract

Abstract. In this paper, we prove some new dynamic inequalities of Hilbert type on time scales. From these inequalities, as special cases, we will formulate some special integral and discrete inequalities. The main results are proved using some algebraic inequalities, Hölder's inequality, Jensen's inequality and a chain rule on time scales.Mathematics subject classification (2010): 26D15, 34A40, 39A12, 34N05.

Some Dynamic Inequalities of Hilbert’s Type

“…Following this trend and to develop the study of dynamic inequalities on time scales, we will prove some new inequalities of Hilbert's type on time scales, namely, we prove time scale versions of inequalities (9) and (11) on time scale T. ese inequalities can be considered as extensions and generalizations of some Hilbert-type inequalities proved in [10]. We also derive some inequalities on time scale as special cases.…”

“…In [10], the authors deduced several generalizations of inequalities (1) and (3) on time scales, namely, they proved that if h and l ≥ 1 are real numbers,…”

Dynamic Inequalities in Quotients with General Kernels and Measures

“…is available for all Δμ 2 -integrable f : Ω 2 → ℝ such that f ðΩ 2 Þ ⊂ I and Φ ∈ CðI, ℝÞ is a convex function. For development of dynamic inequalities on time scale calculus, we refer the reader to articles [11][12][13][14][15][16][17][18]. The article is regimented as follows.…”

Some dynamic Hilbert-type inequalities for two variables on time scales

“…Motivated by the above results, our major aim in this paper is to establish some dynamic Hilbert-type inequalities in two separate variables on time scales. These inequalities can be considered as extensions and generalizations of some Hilbert-type inequalities proved in [7] for the two-dimensional on time scales.…”

“…In the past few years, several researchers have suggested the study of dynamic time scale inequalities. In [7] the authors deduced some generalizations of the inequalities ( 1) and…”