2025/04/11 by Kaur, Parneet, Lal, Rattan, Kumar, Ankit +1
#28A80 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2504.08491
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We first provide a construction of fractal functions for countable data sets and use these functions in the approximation and study of set-valued mappings. We also show the existence and uniqueness of an invariant Borel measure supported on the graph of a set-valued fractal function. In addition, we obtain some effective bounds on the dimensions of the constructed set-valued fractal functions.