Journal
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume 30, Issue 7, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X2250147X
Keywords
Sierpinski Gasket; Box Dimension; Hausdorff Dimension; Bounded Variation
Funding
- University Grants Commission (UGC), India
Ask authors/readers for more resources
In this study, we estimate the upper and lower box dimensions of the graph of a function defined on the Sierpinski gasket under certain continuity conditions. We also provide an upper bound for the Hausdorff dimension and box dimension of the graph of a function with finite energy. Furthermore, we introduce two sets of definitions of bounded variation for a function defined on the Sierpinski gasket and prove that the fractal dimension of the graph of a continuous function of bounded variation is log 3/log 2. We also demonstrate the closure of the class of all bounded variation functions under arithmetic operations and prove that every function of bounded variation is continuous almost everywhere according to the log 3/log 2-dimensional Hausdorff measure.
Under certain continuity conditions, we estimate upper and lower box dimensions of the graph of a function defined on the Sierpinski gasket. We also give an upper bound for Hausdorff dimension and box dimension of the graph of a function having finite energy. Further, we introduce two sets of definitions of bounded variation for a function defined on the Sierpinski gasket. We show that fractal dimension of the graph of a continuous function of bounded variation is log 3/log 2. We also prove that the class of all bounded variation functions is closed under arithmetic operations. Furthermore, we show that every function of bounded variation is continuous almost everywhere in the sense of log 3/log 2-dimensional Hausdorff measure.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available