Related papers: Some integral inequalities on time scales
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.
We introduce the interval Darboux delta integral (shortly, the $ID$ $\Delta$-integral) and the interval Riemann delta integral (shortly, the $IR$ $\Delta$-integral) for interval-valued functions on time scales. Fundamental properties of…
In this note we communicate some important remarks about the concepts of almost periodic time scales and almost periodic functions on time scales that are proposed by Wang and Agarwal in their recent papers (Adv. Difference Equ. (2015)…
We prove some new retarded integral inequalities. The results generalize those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation by using interpolating polynomials in the complex time plane.…
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent…
Sharp inequalitieis of Gruss type for Stieltjes integrals with application in numerical integration are provided.
We device a new method to calculate a large number of Mellin moments of single scale quantities using the systems of differential and/or difference equations obtained by integration-by-parts identities between the corresponding Feynman…
In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…
We obtain some new inequalities of Chebyshev Type.
This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…
By means of the mathematical analysis theory, inequality theory, mathematical induction and the dimension reduction method, under the proper hypotheses, we establish the following cyclic inequalities: \[\sum_{i=1}^{n}…
Physiologic signals have properties across multiple spatial and temporal scales, which can be shown by the complexity-analysis of the coarse-grained physiologic signals by scaling techniques such as the multiscale. Unfortunately, the…
This paper derives practical algorithms, based on Bayesian inference methods, for several data analysis problems common in time series analysis of astronomical and other data. One problem is the determination of the lag between two time…
In this article we consider a method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program.
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
The main goal of this article is to present new types of inequalities refining and reversing inequalities of the harmonic mean of scalars and matrices. Furthermore, implementing the spectral decomposition of positive matrices, we present a…
Based on the local fractional calculus, we establish some new generalizations of H\"{o}lder's inequality. By using it, some results on the generalized integral inequality in fractal space are investigated in detail.