A generalization of Rademacher's theorem on complete differential
A generalization of the Cauchy-Schwarz inequality with eight free parameters.
A generalization of the Gauss-Lucas theorem
Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.
A generalization of the Lagrange mean value theorem to the case of vector-valued mappings.
A generalization of the pre-Grüss inequality and applications to some quadrature formulae.
A generalization of the quasiconvex optimization problem.
A generalization of the theorem of Mauldin
A generalization of the weighted Hardy inequality for a class of integral operators.
A generalized Beckenbach-Dresher inequality and related results.
A generalized Fannes' inequality.
A generalized Halanay inequality for stability of nonlinear neutral functional differential equations.
A generalized integral inequality for twice differentiable mappings
A generalized Lagrange identity and Cauchy-Buniakovsky inequality.
A Generalized Mean-Value Theorem.
A generalized Ostrowski type inequality for a random variable whose probability density function belongs to .
A generalized Ostrowski-Grüss type inequality for twice differentiable mappings and applications.
A generalized sharp Whitney theorem for jets.
Suppose that, for each point x in a given subset E ⊂ Rn, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ Cm,w(Rn) and a finite constant M, such that the m-jet of F at x belongs to f(x) + Mσ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F, M, provided each σ(x) satisfies a condition that we call "Whitnet w-convexity".
A generalized sum-difference inequality and applications to partial difference equations.
A generalized -porous set with a small complement.
A generic condition implying o-minimality for restricted C-functions
We prove that the expansion of the real field by a restricted C-function is generically o-minimal. Such a result was announced by A. Grigoriev, and proved in a different way. Here, we deduce quasi-analyticity from a transcendence condition on Taylor expansions. This then implies o-minimality. The transcendance condition is shown to be generic. As a corollary, we recover in a simple way that there exist o-minimal structures that doesn’t admit analytic cell decomposition, and that there exist incompatible...