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- Title
FRACTAL DIMENSION OF CERTAIN CONTINUOUS FUNCTIONS OF UNBOUNDED VARIATION.
- Authors
LIANG, Y. S.; SU, W. Y.
- Abstract
Continuous functions on closed intervals are composed of bounded variation functions and unbounded variation functions. Fractal dimension of continuous functions with bounded variation must be one-dimensional (1D). While fractal dimension of continuous functions with unbounded variation may be 1 or not. Certain continuous functions of unbounded variation whose fractal dimensions are 1 have been mainly investigated in the paper. A continuous function on a closed interval with finite unbounded variation points has been proved to be 1D. Furthermore, we deal with continuous functions which have infinite unbounded variation points and part of them have been proved to be 1D. Certain examples of 1D continuous functions which have uncountable unbounded variation points have been given in the present paper.
- Subjects
FUNCTIONS of bounded variation; POLYMER structure; NONCRYSTALLINE structure; MATHEMATICAL functions; DISCONTINUOUS functions
- Publication
Fractals, 2017, Vol 25, Issue 1, p-1
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X17500098