Generalised fractal interpolation curved lines and surfaces

Abstract

Rakotch contractions as well as the Matkowski fixed point theorem are used in order to obtain generalised fractal interpolation functions with extensive practical applications so as previous research on bivariable fractal interpolation functions is extended by offering a more comprehensive overview. In particular, generalised fractal interpolation functions by using Rakotch contractions and vertical scaling factors as (continuous) ‘contraction functions' are proposed and an explicit illustrative example is given to show the effectiveness of the proposed methods. Moreover, a method to estimate the lower and upper box-counting dimension of such functions is presented. Furthermore, Rakotch's fixed point theorem instead of Banach's fixed point theorem is used for the existence of generalised bivariate fractal interpolation surfaces. © 2021. CSP - Cambridge, UK; I&S - Florida, USA. All Rights Reserved.