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Approximate high order smoothness. (English) Zbl 0793.26008

The authors introduce the notion of the approximate \(m\)-smoothness of functions and investigate the properties of approximately continuous and approximately \(m\)-smooth functions. The inspiration of the authors was the paper of T. K. Dutta [Acta Math. Acad. Sci. Hung. 40, 29-37 (1982; Zbl 0511.26006)] in which the notion of high order smoothness is introduced.
“…the purpose of this paper is to show that results analogous to those of Dutta carry over to this setting…”.
Reviewer: R.Pawlak (Łódź)

MSC:

26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
28A99 Classical measure theory

Citations:

Zbl 0511.26006
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Full Text: DOI

References:

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