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La mesurabilité des fonctions de deux variables et de la superposition F(x, f(x))

Zbigniew Grande — 1978

TABLE DES MATIÈRESIntroduction.................................................................................................................................................................. 5Chapitre I. Conditions équivalentes à la mesurabilité d'une fonction de deux variables..................................... 7Chapitre II. Conditions suffisantes pour la mesurabilité des fonctions de deux variables................................. 18Chapitre III. Mesurabilité des fonctions de deux variables...

On the almost monotone convergence of sequences of continuous functions

Zbigniew Grande — 2011

Open Mathematics

A sequence (f n)n of functions f n: X → ℝ almost decreases (increases) to a function f: X → ℝ if it pointwise converges to f and for each point x ∈ X there is a positive integer n(x) such that f n+1(x) ≤ f n (x) (f n+1(x) ≥ f n(x)) for n ≥ n(x). In this article I investigate this convergence in some families of continuous functions.

On some equations y'(x) = f(x,y(h(x)+g(y(x))))

Zbigniew Grande — 2011

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In [4] W. Li and S.S. Cheng prove a Picard type existence and uniqueness theorem for iterative differential equations of the form y'(x) = f(x,y(h(x)+g(y(x)))). In this article I show some analogue of this result for a larger class of functions f (also discontinuous), in which a unique differentiable solution of considered Cauchy's problem is obtained.

On a subclass of the family of Darboux functions

Zbigniew Grande — 2009

Colloquium Mathematicae

We investigate functions f: I → ℝ (where I is an open interval) such that for all u,v ∈ I with u < v and f(u) ≠ f(v) and each c ∈ (min(f(u),f(v)),max(f(u),f(v))) there is a point w ∈ (u,v) such that f(w) = c and f is approximately continuous at w.

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