A new method for the construction of fractals via best proximity point theory. (English) Zbl 07920580
Summary: 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 [the third author et al., Chaos Solitons Fractals 146, Article ID 110850, 7 p. (2021; Zbl 1498.28007)] 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.
MSC:
| 28A80 | Fractals |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 47H10 | Fixed-point theorems |
Citations:
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