A ONE-DIMENSIONAL CONTINUOUS FUNCTION WITH UNBOUNDED VARIATION
Author:
YANG DONG1,
YUAN XIA1ORCID,
ZHANG KANG1ORCID,
WU SHIWEI1ORCID,
ZHAO CHUNXIA1
Affiliation:
1. School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Abstract
In this paper, we consider a function with only one unbounded variation point and study the box dimension of its graph. We prove that the function is continuous and differentiable on a certain interval. Moreover, we show that the function is of unbounded variation on the domain of definition. Using our techniques, we also estimate the box dimension of the graph of the function.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province
Fundamental Research Funds for the Central Universities
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
Cited by
1 articles.
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