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
paper · pdf · doi:10.48550/arxiv.1809.09393
openalex publication_date 2018/09/25 · 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\nharmonic function on the Sierpi 'nski gasket. Also we get upper and lower\nbounds for the box dimension of graph of functions that belongs to\n\dom(\E), that is, all finite energy functionals on the\nSierpi 'nski gasket. Further, we show the existence of fractal functions in the\nfunction space \dom(\E) with the help of fractal interpolation\nfunctions. Moreover, we provide bounds for the box dimension of some functions\nthat belong to the family of continuous functions and arise as fractal\ninterpolation functions.\n