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...
A geometrical proof of a new inequality for the gamma function.
A global uniqueness result for fractional order implicit differential equations
In this paper we investigate the global existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of implicit hyperbolic fractional order differential equations by using a nonlinear alternative of Leray-Schauder type for contraction maps on Fréchet spaces.
A Grüss type inequality for sequences of vectors in inner product spaces and applications.
A Grüss-type inequality and its applications.
A Hake-type property for the -integral and its relation to other integration processes
A Hardy inequality with remainder terms in the Heisenberg group and the weighted eigenvalue problem.
A Hardy type inequality for functions
We consider functions , where is a smooth bounded domain, and is an integer. For all , such that , we prove that with , where is a smooth positive function which coincides with dist near , and denotes any partial differential operator of order .
A hierarchy in the family of real surjective functions
This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The...
A Hilbert integral-type inequality with parameters.
A Hilbert's inequality with a best constant factor.
A Hilbert-type integral inequality in the whole plane with the homogeneous kernel of degree .
A Hilbert-type integral inequality with a hybrid kernel and its applications
We prove a multi-parameter Hilbert-type integral inequality with a hybrid kernel. We describe the best constant in the inequality in terms of hypergeometric functions. Some equivalent forms of the inequalities are also studied. By specifying parameter values we obtain results proved by other authors as well as many new inequalities.
A historical outline of the theorem of implicit functions.