DOI: 10.24193/fpt-ro.2024.2.01

Authors: Mustafa Aslantas, Hakan Sahin and Ishak Altun

Abstract: 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 λ-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.

Key Words and Phrases: Fractals, best proximity point, P-property, iterated function

2010 Mathematics Subject Classification: 28A80, 54H25, 47H10.

Published on-line: June 15th, 2024.

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