In this paper, Ω is a bounded domain in R (N ≥ 2), with a Lipschitz continuous boundary. The unit normal to ∂Ω outward to Ω is denoted by n. We denote by x·y the usual Euclidean product of two vectors (x, y) ∈ R × R ; the associated Euclidean norm is written |.|. The Lebesgue measure of a measurable subset E in R is denoted by |E|; σ is the Lebesgue measure on ∂Ω (i.e. the (N−1)-dimensional Hau...

hold. The facts above are well-known as the classical Shannon sampling theorem initially proved by Ogura [10]. Ashino and Mandai [1] generalized the sampling theorem in Lebesgue spaces L0(R) for 1 < p0 < ∞. Their generalized sampling theorem is the following. Theorem 1.1 ([1]). Let r > 0 and 1 < p0 < ∞. Then for all f ∈ L 0(R) with supp f̂ ⊂ [−rπ, rπ], we have the norm inequality C p r ‖f‖Lp0(Rn...

In this paper, we  present a version of Favard's inequality for special case and then generalize it for the Sugeno integral in fuzzy measure space $(X,Sigma,mu)$, where $mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.

We obtain precise estimates relating the phase space and the parameter space of analytic families of unimodal maps, which generalize the case of the quadratic family obtained in [AM1]. This result implies a statistical description of the dynamics of typical analytic quasiquadratic maps which is much sharper than what was previously known: as an example, we can conclude that the recurrence of th...

In this paper, we look for sufficient conditions on the lateral surface of the domain and on the coefficients of the boundary conditions of a N−space dimensional linear parabolic equation, in order to obtain existence, uniqueness and maximal regularity of the solution in a Hilbertian anisotropic Sobolev space when the right hand side of the equation is in a Lebesgue space. This work is an exten...