P-adic continuously differentiable functions of several variables.
Parametrization of Carathéodory multifunctions
Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions
We consider a multifunction , where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.
Peano type theorem for random fuzzy initial value problem
In this paper we consider the random fuzzy differential equations and show their application by an example. Under suitable conditions the Peano type theorem on existence of solutions is proved. For our purposes, a notion of ε-solution is exploited.
Periodic oscillation of fuzzy Cohen-Grossberg neural networks with distributed delay and variable coefficients.
Periodicity, almost periodicity for time scales and related functions
In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.
Polynomial inequalities on general subsets of
Polynomial selections and separation by polynomials
K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
Polynomial set-valued functions
The aim of this paper is to give a necessary and sufficient condition for a set-valued function to be a polynomial s.v. function of order at most 2.
Positive semidefinite matrices, exponential convexity for majorization, and related Cauchy means.
Positively homogeneous functions and the Łojasiewicz gradient inequality
It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.
Preparation theorems for matrix valued functions
We generalize the Malgrange preparation theorem to matrix valued functions satisfying the condition that vanishes to finite order at . Then we can factor near (0,0), where is inversible and is polynomial function of depending on . The preparation is (essentially) unique, up to functions vanishing to infinite order at , if we impose some additional conditions on . We also have a generalization of the division theorem, and analytic versions generalizing the Weierstrass preparation...
Preparation theorems for systems
Prevalence of "nowhere analyticity"
This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study to Gevrey classes of functions.
Principe de la phase résonnante
On donne une variante du principe de la phase stationnaire, où l’intégrale est remplacée par une sommation sur le réseau cubique de maille égale à l’unité de phase.
Prolongement dans des classes ultradifférentiables et propriétés de régularité des compacts de
Considering jets, or functions, belonging to some strongly non-quasianalytic Carleman class on compact subsets of , we extend them to the whole space with a loss of Carleman regularity. This loss is related to geometric conditions refining Łojasiewicz’s “regular separation” or Whitney’s “property (P)”.
Proof for A conjecture on general means.
Proof of one optimal inequality for generalized logarithmic, arithmetic, and geometric means.
Pseudo-operations on finite intervals.