2018/09/25 by Abhilash Sahu, Sahu, Abhilash, Amit Priyadarshi +1
Computer Science · Mathematics · Physics and Astronomy · #28A80 #Advanced Mathematical Theories and Applications #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Theoretical and Computational Physics #Topological and Geometric Data Analysis #math.MG #msc:28A80
paper · pdf · doi:10.48550/arxiv.1809.09393
17 pages, 1 figure
arxiv created 2018/09/25 · openalex publication_date 2018/09/25 · arxiv updated 2018/09/26 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
In this paper, we have obtained bounds for the box dimension of graph of harmonic function on the Sierpiński gasket. Also we get upper and lower bounds for the box dimension of graph of functions that belongs to dom(E), that is, all finite energy functionals on the Sierpiński gasket. Further, we show the existence of fractal functions in the function space dom(E) with the help of fractal interpolation functions. Moreover, we provide bounds for the box dimension of some functions that belong to the family of continuous functions and arise as fractal interpolation functions.