# A New Class of Monotone/Convex Rational Fractal Function

Source: [A New Class of Monotone/Convex Rational Fractal Function](<https://www.sota2.com/research/paper/68fa55341e209131ce9922d2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T13:27:41.818Z

Authors: S. K. Katiyar, A. K. B. Chand

Published: 2018-09-27T13:49:15.000Z

## Abstract

This paper presents a description and analysis of a rational cubic spline FIF (RCSFIF) that has two shape parameters in each subinterval when it is defined implicitly. To be precise, we consider the iterated function system (IFS) with $q\_n=\\frac{P\_n}{Q\_n}$, $n \\in \\mathbb{N}\_{N-1}$, where $P\_n(x)$ are cubic polynomials to be determined through interpolatory conditions of the corresponding FIF and $Q\_n(x)$ are preassigned quadratic polynomials each containing two free shape/rationality parameters. We establish the convergence of the proposed RCSFIF $g$ to the original function $\\Phi \\in \\mathcal{C}^3(I)$ with respect to the uniform norm. We also provide the sufficient conditions for an automatic selection of the rational IFS parameters to preserve monotonicity and convexity of a prescribed set of data points. We consider some examples to illustrate the developed fractal interpolation scheme and its shape preserving aspects.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1809.10682>)

[PDF](<https://arxiv.org/pdf/1809.10682.pdf>)