TY - JOUR

T1 - Baire one path systems, Baire* one path systems and path derivatives

AU - Alikhani-Koopaei, Aliasghar

N1 - Publisher Copyright:
© 2023 World Scientific Publishing Co. Pte Ltd. All rights reserved.

PY - 2023/11/1

Y1 - 2023/11/1

N2 - In this paper, we study the class of Baire one path systems as a metric space and as a multifunction and show that some known classes of path systems such as continuous path systems, composite continuous path systems, and first return path systems are subclasses of the class of Baire one path systems. In particular, we show that a path system is composite continuous if and only if it is Baire* one path system. We also show that for a composite continuous path system E = {Ex : x ∈ [0, 1]}, the upper (respectively, lower) extreme path derivatives f'E(respectively, f'E) of a function f ∈ B1 are upper (respectively, lower) Baire two functions, and when f is E-differentiable, f'E ∈ B2.

AB - In this paper, we study the class of Baire one path systems as a metric space and as a multifunction and show that some known classes of path systems such as continuous path systems, composite continuous path systems, and first return path systems are subclasses of the class of Baire one path systems. In particular, we show that a path system is composite continuous if and only if it is Baire* one path system. We also show that for a composite continuous path system E = {Ex : x ∈ [0, 1]}, the upper (respectively, lower) extreme path derivatives f'E(respectively, f'E) of a function f ∈ B1 are upper (respectively, lower) Baire two functions, and when f is E-differentiable, f'E ∈ B2.

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U2 - 10.1142/S1793557123501991

DO - 10.1142/S1793557123501991

M3 - Article

AN - SCOPUS:85170680713

SN - 1793-5571

VL - 16

JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

IS - 11

M1 - 2350199

ER -