This work addresses the asymptotic stability for a class of impulsive cellular neural networks with time-varying delays and reaction-diffusion. By using the impulsive integral inequality of Gronwall-Bellman type and Hardy-Sobolev inequality as well as piecewise continuous Lyapunov functions, we summarize some new and concise sufficient conditions ensuring the global exponential asymptotic stabi...

We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality of H. G. Hardy from 1918. We also obtain new results involving fractional derivatives of Canavati and Caputo types as ...

A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...

In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on Hölder-α domains, where the weights are powers of distance to boundary. We obtain results regarding divergence equation’s solvability, improved Poincaré, fractional Korn inequalities. The proofs based local-to-global argument that involves kind atomic decomposition functions validity discrete Hardy-...

In this paper, we prove capacitary versions of the fractional Sobolev–Poincaré inequalities. We characterize localized variant boundary inequalities through uniform fatness condition domain in $$\mathbb {R}^n$$ . Existence type results on Hardy inequality supercritical case $$sp>n$$ for $$s\in (0,1)$$ , $$p>1$$ are established.

The aim of this paper is to establish higher order Poincaré-Sobolev, Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on Siegel domains complex hyperbolic spaces using the method Helgason-Fourier analysis spaces. Firstly, we give a factorization theorem for operators space which closely related Geller's operator, as well CR invariant differential Heisenberg group sphere. (See Theorem 1....

Abstract By means of the weight functions, idea introducing parameters and technique real analysis, a new Hardy–Hilbert-type integral inequality with homogeneous kernel $\frac{1}{(x + y)^{\lambda}}\ (\lambda &gt; 0)$ 1(x+y<m...