2020/10/05 by S. Verma, Verma, S., A. Sahu +1
Computer Science · Mathematics · #26A45 #28A80 #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2010.01780
openalex publication_date 2020/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Under certain continuity conditions, we estimate upper and lower box dimension of graph of a function defined on the Sierpinski gasket. We also give an upper bound for Hausdorff dimension and box dimension of graph of 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 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.