Approximate high order smoothness
Copyright policy )Approximate high order smoothness
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 \textit{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. ``\dots the purpose of this paper is to show that results analogous to those of Dutta carry over to this setting\dots''.
- North Carolina State University United States
- North Carolina Agricultural and Technical State University United States
- St. Olaf College United States
- Eötvös Loránd University Hungary
Darboux property, approximate Peano derivative, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, \(\text{Baire}^* 1\) function, approximate \(m\)-smoothness, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, Classical measure theory
Darboux property, approximate Peano derivative, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, \(\text{Baire}^* 1\) function, approximate \(m\)-smoothness, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, Classical measure theory
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