Related papers: Some integral inequalities on time scales
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
In this paper, we establish some new Hadamard type inequalities using elementary well known inequalities for functions whose inequalities absolute values are {\alpha}-, m-, ({\alpha},m)-logarithmically convex.
We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in…
Time series anomaly detection is an important task, with applications in a broad variety of domains. Many approaches have been proposed in recent years, but often they require that the length of the anomalies be known in advance and…
For a large class of systems of o.d.e.'s which have first integrals, the method of arrays yields the following results: i) The first integrals $I$ can be found by solving systems of linear equations. ii) How the first integral $I$ responds…
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy inequality, here we discuss the corresponding Hardy-Rellich and Rellich inequality versions in the integral form. The obtained sharp Hardy-Rellich…
This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future…
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…
Inequalities for exponential sums are studied. Our results improve an old result of G. Halasz and a recent result of G. Kos. We prove several other essentially sharp related results in this paper.
This paper is discussing about the notion of some new types of convergences namely $I$-convergence and $I^*$-convergence of a $\Delta$-measurable function $f$ on time scales $T$ by considering ideal on time scales $T$. This idea is further…
In this paper, we will prove several new inequalities of Hardy's types with explicit constants. The main results will be proved by making use of some generalizations of Opial's type inequalities and H\"older's inequality. To the best of the…
The study of what we now call Sobolev inequalities has been studied for almost a century in various forms, while it has been eighty years since Sobolev's seminal mathematical contributions. Yet there are still things we don't understand…
This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…
In this paper we consider a new kind of inequality related to fractional integration, motivated by Gressman's paper. Based on it we investigate its multilinear analogue inequalities. Combining with the Gressman's work on multilinear…
Unfair metrical task systems are a generalization of online metrical task systems. In this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain improved randomized…
Multivariate time series alignment is critical for ensuring coherent analysis across variables, but missing values and timestamp inconsistencies make this task highly challenging. Existing approaches often rely on prior imputation, which…
We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary…
We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.