Open AccessThe Relation between Hölder Continuous Function of Order α ∈ (0,1) and Function of Bounded Variation
Author(s) -
Supriyadi Wibowo,
Vika Yugi Kurniawan,
Siswanto Siswanto
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1490/1/012043
Subject(s) - bounded variation , hölder condition , continuous function (set theory) , bounded function , mathematics , function (biology) , order (exchange) , pure mathematics , variation (astronomy) , mathematical analysis , combinatorics , physics , finance , evolutionary biology , astrophysics , economics , biology
The Cantor ternary function is the most famous example of a continuous function of bounded variation for which it satisfies the Holder continuous function of order α = log 3 2, but does not satisfy for order α = 1. In this paper, based on previous work of Hölder continuous function of order α ∈ (0, 1) and using F α - calculus on fractal set F , we show the relation between the Hölder continuous function of order α ∈ (0, 1) and function of bounded variation. In particular, we give the necessary and sufficient condition for the variation of function satisfies Hölder condition or bi-Hölder condition.