TY - JOUR

T1 - Path derived numbers and path derivatives of continuous functions with respect to continuous systems of paths

AU - Alikhani-Koopaei, Aliasghar

N1 - Funding Information:
Key Words: Derived numbers, First Return Derivatives, Path systems, Path Derivatives, Typical Continuous functions Mathematical Reviews subject classification: 26A24, 26A21, 26A27, 26A03, 26A15 Received by the editors April 25, 2003 Communicated by: B. S. Thomson ∗This work was partially supported through a Research and Development Grant from Berks-Lehigh Valley College of the Pennsylvania State University

PY - 2004

Y1 - 2004

N2 - V. Jarnik showed that a typical continuous function on the unit interval [0, 1] has every extended real number as a derived number at every point of [0, 1]. In this paper we classify the derived numbers of a continuous function and study the likelihood of Jarnik's Theorem for path derived numbers of a continuous system of paths. We also provide some results indicating that some of the nice behaviors of first return derivatives are shared by path derivatives of continuous functions when the path system is continuous.

AB - V. Jarnik showed that a typical continuous function on the unit interval [0, 1] has every extended real number as a derived number at every point of [0, 1]. In this paper we classify the derived numbers of a continuous function and study the likelihood of Jarnik's Theorem for path derived numbers of a continuous system of paths. We also provide some results indicating that some of the nice behaviors of first return derivatives are shared by path derivatives of continuous functions when the path system is continuous.

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U2 - 10.14321/realanalexch.29.1.0355

DO - 10.14321/realanalexch.29.1.0355

M3 - Article

AN - SCOPUS:85032353240

SN - 0147-1937

VL - 29

SP - 355

EP - 364

JO - Real Analysis Exchange

JF - Real Analysis Exchange

IS - 1

ER -