A NEW METHOD FOR THE CONSTRUCTION OF FRACTALS VIA BEST PROXIMITY POINT THEORY - Aslantas, Mustafa; Sahin, Hakan; Altun, Ishak (House Book Science-Casa Cartii Stiinta, 2024)
In this paper, taking into account the P-property in the best proximity point theory, we present a new and interesting construction method that is different from the method given in [3] for fractals. First, we introduce the concept of a generalized iterated function system (in short GIFS) constructed by a finite family of lambda-contractions. Then, we present our main theorem in which sufficient conditions are determined to obtain a fractal which is also an attractor of the mentioned system. Finally, we support our results with some illustrative and attractive examples.
Keywords: Fractals; best proximity point; P-property; iterated function systems