Related papers: Two Dimensional Integral Inequalities on Time Scal…
We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…
We study certain double--series inequalities, which are motivated by weighted Hardy inequalities.
This article revisits the historiography of the problem of inertial frames. Specifically, the case of the twins in the clock paradox is considered to see that some resolutions implicitly assume inertiality for the non-accelerating twin. If…
In this paper we give refinements of some convex and log-convex moment inequalities of the first and second order using a special kind of positive semi-definite form. An open problem concerning eight parameter refinement of second order is…
We give an elementary estimate that entails and generalises numerous Korn inequalities scattered in the literature. As special instances, we obtain general Korn-type inequalities involving normal or tangential trace components, or lower…
This article discusses several matters related to Sobolev, Poincare, and isoperimetric inequalities in various settings.
This work establishes a comprehensive analytical framework for studying implicit fractional differential systems with distributed memory and time delays. We develop novel fractional integral inequalities of Gr\"onwall--Wendroff type that…
In [Bull. Acad. Polon. Sci. S\'{e}r. Sci. Math. 29 (1981), no.~7-8, 367--370], Philos proved the following result: Let $f:[t_{0},\infty)_{\mathbb{R}}\to\mathbb{R}$ be an $n$-times differentiable function such that $f^{(n)}(t)\leq0$…
The aim of this note is to give two new conceptual proofs of Ionescu-Weitzenb\"ock's inequality. The first one, which is a vector proof, provides us a geometric interpretation of the difference between the two sides of this inequality and…
We show that Caffarelli-Kohn-Nirenberg first order interpolation inequalities as well as weighted trace inequalities in $\mathbb{R}^n \times \mathbb{R}_+$ admit a better range of power weights if we restrict ourselves to the space of…
In this short notes we will derive an inequality for scaled $q^{-1}$-Hermite orthogonal polynomials of Ismail and Masson, an inequality for scaled Stieltjes-Wigert, two inequalities for Ramanujan function and two definite integrals for…
We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one hand Weyl bounds; and on the other hands bounds on the…
In this paper we give new deviation inequalities of Bernstein's type for the partial sums of weakly dependent time series. The loss from the independent case is studied carefully. We give non mixing examples such that dynamical systems and…
Recently a new class of time-dependent Bell inequalities in Wigner form was introduced. The structure of the inequalities allows experimental studies of quantum and open quantum systems in external fields. In this paper we study the…
In this paper, we establish various inequalities for some mappings that are linked with the illustrious Hermite-Hadamard integral inequality for mappings whose absolute values belong to the class K?;s m;1 and K?;s m;2.
Time scales are a model of time, where the continuous and the discrete time cases are considered and merged into the same framework. In this paper some basic definitions of the time scale calculus are presented. Simultaneously, a package in…
We establish an analogue of Wolff's theorem on ideals in $H^{\infty}(\mathbb{D})$ for the multiplier algebra of weighted Dirichlet space.
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…