Rational quadratic trigonometric spline fractal interpolation functions with variable scalings

Fractal interpolation function (FIF) constructed through an iterated function system is more versatile than any classical spline interpolation. In this paper, we propose a novel C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document}-rational quadratic trigonometric spline FIF with variable scaling, where the numerator and denominator of rational function are quadratic trigonometric polynomials with two shape parameters in every subinterval. The error and convergence analysis of the proposed rational trigonometric fractal interpolant are studied for data generating function in C3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^3$$\end{document}. We deduce sufficient conditions based on the parameters of the rational quadratic trigonometric spline FIF to preserve positivity, monotonicity, and range restrictions features of the concerned data sets. Numerical examples are presented to supplement the shape preserving results based on a restricted class of scaling functions and minimum values of the shape parameters.