Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors

摘要

We estimate the bounds for box-counting dimension of hidden variable fractal interpolation functions (HVFIFs) and hidden variable bivariate fractal interpolation functions (HVBFIFs) with four function contractivity factors and present analytic properties of HVFIFs which are constructed to ensure more flexibility and diversity in modeling natural phenomena. Firstly, we construct the HVFIFs and analyze their smoothness and stability. Secondly, we obtain the lower and upper bounds for box-counting dimension of the HVFIFs. Finally, in the similar way, we get the lower and upper bounds for box-counting dimension of HVBFIFs in [Yun CH and Li MK, Hidden variable bivariate fractal interpolation functions and errors on perturbations of function vertical scaling factors, AEJM, 2019; 12(2), doi:10.1142/s 1793557119500219]. (C) 2020 Elsevier Ltd. All rights reserved.