Abstract
AbstractIn this paper, we prove the existence of the attractors for Reich’s iterated function systems by virtue of a Banach-like fixed point theorem. As a result, under the condition that the Reich contractions discussed are continuous, we give an affirmative answer to an open question posed by Singh et al. in 2009. In addition, we formulate a collage theorem for Reich’s iterated function systems.
Highlights
Fixed point theory plays an important role in iterated function systems as well as fractals
We obtain the attractors for a number of new iterated function systems by virtue of a Banachlike fixed point theorem concerning such generalized contractive mappings
Under the condition that the Reich contractions discussed are continuous, we give an affirmative answer to the above-mentioned open question posed by Singh et al In addition, we show that the attractor, either for Hutchinson’s iterated function system or for the K -iterated function system, turns out to be the same as for Reich’s iterated function system which can be deduced by means of such a Banach-like fixed point theorem concerning such generalized contractive mappings
Summary
Fixed point theory (see, for instance, [ – ]) plays an important role in iterated function systems as well as fractals (see [ – ]). We obtain the attractors for a number of new iterated function systems by virtue of a Banachlike fixed point theorem concerning such generalized contractive mappings.
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