On approximately monotone and approximately Hölder functions
Angshuman R. Goswami,
Zsolt Páles
Abstract:A real valued function f defined on a real open interval I is called Φ-monotone if, for all x, y ∈ I with x ≤ y it satisfies f (x) ≤ f (y) + Φ(y − x), where Φ : [0, ℓ(I)[ → R+ is a given nonnegative error function, where ℓ(I) denotes the length of the interval I. If f and −f are simultaneously Φ-monotone, then f is said to be a Φ-Hölder function.In the main results of the paper, we describe structural properties of these function classes, determine the error function which is the most optimal one. We show that… Show more
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