A new approach to fractals via best proximity point

Abstract

• In this paper, we introduce the concept of proximal IFS generated by a.nite set of proximal contractions to expand the concept of IFS, one of the most com- mon methods of creating fractals. Thus, as a new method of obtaining fractal, we present a result showing that the proximal IFS has a unique best attrac- tor under certain conditions on metric spaces. Hence, this study is important because it presents new approach to fractals through best proximity points. In this paper, we present a new approach to fractals through best proximity points, inspired by the remarkable relationship between fixed point theory and fractal theory. In this way, we introduce the concept of proximal IFS generated by a finite set of proximal contractions to expand the concept of IFS, one of the most common methods of creating fractals. Thus, as a new method of obtaining fractal we present a result showing that the proximal IFS has a unique best attractor under the certain conditions on metric spaces. To support our new result an illustrative example is given.