Abstract
The aim of this paper is to construct a fractal with the help of a finite family of generalizedF-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup ofb-metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Our results unify, generalize, and extend various results in the existing literature.
Highlights
Introduction and PreliminariesIterated function systems are method of constructing fractals and are based on the mathematical foundations laid by Hutchinson [1]
He showed that Hutchinson operator constructed with the help of a finite system of contraction mappings defined on Euclidean space Rn has closed and bounded subset of Rn as its fixed point, called attractor of iterated function system
Banach contraction principle [3] is of paramount importance in metrical fixed point theory with a wide range of applications, including iterative methods for solving linear, nonlinear, differential, integral, and difference equations
Summary
Introduction and PreliminariesIterated function systems are method of constructing fractals and are based on the mathematical foundations laid by Hutchinson [1]. He showed that Hutchinson operator constructed with the help of a finite system of contraction mappings defined on Euclidean space Rn has closed and bounded subset of Rn as its fixed point, called attractor of iterated function system (see [2]). Many researchers have obtained fixed point results for single and multivalued mappings defined on metrics spaces.
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