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The monomial difference majorized by single variable function

Budzik D.

Demonstratio Mathematica

2015

Vol. 48, nr 1

73--76

We deal with the monomial difference (…) assuming that its norm is majorized by some function depending upon the variable y.

On Some Stability Properties of Monomial Functions

Budzik D.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2003

Vol. 9

17--23

A map M defined on a semigroup (group, Banach space etc.) and taking values in an Abelian group is called monomial of degree at most n whenever [formula]. We deal with the following stability problem for monomial mappings: given two functions F and ƒ satisfying the inequality [formula], we are looking for conditions admitting the existence of a nonnegative constant α such that [formula].

Stability properties of monomial functions

Budzik D.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2002

[Z] 42(2)

183-198

A map M defined on a semigroup (group, Banach space etc.) S and taking values in an Abelian group is called monomial of degree at most n whenever Δny M (x) = n!M (y), where Δny stands for the n-th iterate of the usual difference operator Δy. We are looking for conditions upon a map F from S into a real normed linear space, controlled by ƒ in the sense that || n!F (y) - Δny F(x) || ≤ n!ƒ (y) - Δny ƒ(x), to be uniformly approximated by monomial mapping of degree at most n.