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Some new nonlinear retarded sum-difference inequalities with applications [PDF]

Advances in Difference Equations, 2011
The main objective of this paper is to establish some new retarded nonlinear sum-difference inequalities with two independent variables, which provide explicit bounds on unknown functions.
Cheung Wing-Sum, Li Zizun, Wang Wu-Sheng
core   +2 more sources

Poincar\'e inequalities for mutually singular measures [PDF]

Analysis and Geometry in Metric Spaces, 2014
Using an inverse system of metric graphs as in: J. Cheeger and B. Kleiner, "Inverse limit spaces satisfying a Poincar\'e inequality", we provide a simple example of a metric space $X$ that admits Poincar\'e inequalities for a continuum of mutually ...
Schioppa, Andrea
core   +3 more sources

Philebus 23c-26d: Peras, Apeiron, and Meikton as Measure Theory

Plato, 2021
At Philebus 23c4-26d10 Socrates makes a division into three kinds: Unbounded (apeiron), Bound (peras), and Mix (meikton). I review problems for the main interpretations of Unbounded and Mix and review kinds of scales defined in abstract measurement ...
George Rudebusch
doaj   +1 more source

LOWER BOUNDS ON LP QUASI‐NORMS AND THE UNIFORM SUBLEVEL SET PROBLEM

Mathematika, Volume 67, Issue 2, Page 296-323, April 2021., 2021
Abstract Recently, Steinerberger (Potential Analysis, 2020) proved a uniform inequality for the Laplacian serving as a counterpoint to the standard uniform sublevel set inequality which is known to fail for the Laplacian. In this paper, we observe that many inequalities of this type follow from a uniform lower bound on the L1 norm, and give an ...
John Green
wiley   +1 more source

Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications

Open Mathematics, 2023
Let m∈Nm\in {\mathbb{N}} and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces Wm,φ(Rn){W}^{m,\varphi }\left({{\mathbb{R}}}^{n}).
Wu Ruimin, Wang Songbai
doaj   +1 more source

Lp Hardy's identities and inequalities for Dunkl operators

Advanced Nonlinear Studies, 2022
The main purpose of this article is to establish the Lp{L}^{p} Hardy’s identities and inequalities for Dunkl operator on any finite balls and the entire space RN{{\mathbb{R}}}^{N}. We also prove Hardy’s identities and inequalities on certain domains with
Wang Jianxiong
doaj   +1 more source

Gauss Lucas theorem and Bernstein-type inequalities for polynomials

Acta Universitatis Sapientiae: Mathematica, 2022
According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central importance in the geometry of critical points in the analytic theory of polynomials.
Ali Liyaqat, Rather N. A., Gulzar Suhail
doaj   +1 more source

Spectral Stability of the Neumann Laplacian [PDF]

, 2001
We prove the equivalence of Hardy- and Sobolev-type inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space. We also
Burenkov, V. I., Davies, E. B.
core   +2 more sources

Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function

Open Mathematics, 2020
The primary objective of this research is to establish the generalized fractional integral inequalities of Hermite-Hadamard-type for MT-convex functions and to explore some new Hermite-Hadamard-type inequalities in a form of Riemann-Liouville fractional ...
Han Jiangfeng, Mohammed Pshtiwan Othman, Zeng Huidan   +2 more
doaj   +1 more source