Some results on Continuous dependence of fractal functions on the Sierpi\'nski gasket

In this article, we show that $\alpha$-fractal functions defined on Sierpi\'nski gasket (denoted by $\triangle$) depend continuously on the parameters involved in the construction. In the latter part of this article, the continuous dependence of parameters on $\alpha$-fractal functions defined on $\triangle$ is shown graphically.

[1]  Saurabh Verma,et al.  Analytical and dimensional properties of fractal interpolation functions on the Sierpiński gasket , 2023, Fractional Calculus and Applied Analysis.

[2]  Saurabh Verma,et al.  Bernstein super fractal interpolation function for countable data systems , 2022, Numerical Algorithms.

[3]  Subhash Chandra,et al.  ON FRACTAL DIMENSIONS OF FRACTAL FUNCTIONS USING FUNCTION SPACES , 2022, Bulletin of the Australian Mathematical Society.

[4]  R. Mohapatra,et al.  Iteration of Operators with Contractive Mutual Relations of Kannan Type , 2022, Mathematics.

[5]  Saurabh Verma,et al.  Fractal interpolation function on products of the Sierpiński gaskets , 2022, Chaos, Solitons & Fractals.

[6]  Saurabh Verma,et al.  Vector-valued fractal functions: Fractal dimension and fractional calculus , 2022, Indagationes Mathematicae.

[7]  Saurabh Verma,et al.  Fractal dimension for a class of complex-valued fractal interpolation functions , 2022, 2204.03622.

[8]  S. Abbas,et al.  Analysis of fractal dimension of mixed Riemann-Liouville integral , 2022, Numerical Algorithms.

[9]  A. Priyadarshi,et al.  Graphs of continuous functions and fractal dimensions , 2022, Chaos, Solitons & Fractals.

[10]  T. Som,et al.  Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {L}}^p$$\end{document}-Approximation Using Fractal Functio , 2022, Results in Mathematics.

[11]  Saurabh Verma,et al.  Fractal dimension of Katugampola fractional integral of vector-valued functions , 2021, The European Physical Journal Special Topics.

[12]  A. Sahu,et al.  Bounded variation on the Sierpinski Gasket , 2020, Fractals.

[13]  SONG-IL Ri.  Fractal functions on the Sierpinski Gasket , 2020 .

[14]  A. Priyadarshi,et al.  On the box-counting dimension of graphs of harmonic functions on the Sierpiński gasket , 2020 .

[15]  S. Abbas,et al.  THE CALCULUS OF BIVARIATE FRACTAL INTERPOLATION SURFACES , 2020, 2005.06241.

[16]  P. Massopust,et al.  Dimension preserving approximation , 2020, Aequationes mathematicae.

[17]  R. Strichartz.  Differential Equations on Fractals , 2018 .

[18]  A. Priyadarshi.  Lower bound on the Hausdorff dimension of a set of complex continued fractions , 2017 .

[19]  S. A. Prasad.  Node insertion in Coalescence Fractal Interpolation Function , 2013 .

[20]  H. Ruan,et al.  Some properties of fractal interpolation functions on Sierpinski gasket , 2011 .

[21]  H. Ruan.  FRACTAL INTERPOLATION FUNCTIONS ON POST CRITICALLY FINITE SELF-SIMILAR SETS , 2010 .

[22]  M. Navascués.  Fractal Polynomial Interpolation , 2005 .

[23]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[24]  Michael F. Barnsley,et al.  Fractal functions and interpolation , 1986 .

[25]  Saurabh Verma,et al.  Non-stationary zipper ˛ -fractal functions and associated fractal operator , 2022 .

[26]  S. Jha,et al.  Dimensional Analysis of α -Fractal Functions , 2021 .

[27]  T. Som,et al.  Fractal dimension of α -fractal function on the Sierpi´nski , 2021 .

[28]  Derya Çelik,et al.  Fractal interpolation on the Sierpinski Gasket , 2008 .

[29]  R. Strichartz.  ANALYSIS ON FRACTALS , 1999 .