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New aspects concerning IFSs consisting of continuous functions satisfying Banach’s orbital condition

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In the paper “Iterated function systems consisting of continuous functions satisfying Banach’s orbital condition” (An. Univ. Timişoara, Ser. Mat.-Inform., in print), Miculescu, Mihail and Savu introduced iterated function systems consisting… Click to show full abstract

In the paper “Iterated function systems consisting of continuous functions satisfying Banach’s orbital condition” (An. Univ. Timişoara, Ser. Mat.-Inform., in print), Miculescu, Mihail and Savu introduced iterated function systems consisting of continuous functions satisfying Banach’s orbital condition and proved that the fractal operator associated to such a system is weakly Picard. The present paper can be considered as a companion of the above mentioned paper. It provides an evaluation of the Hausdorff-Pompeiu distance between the sets of attractors for two systems consisting of continuous functions satisfying Banach’s orbital condition in terms of the uniform distance between the functions of the systems and it states the continuity of the attractors for this type of systems. Some examples are provided.

Keywords: satisfying banach; continuous functions; consisting continuous; functions satisfying; banach orbital; orbital condition

Journal Title: Journal of Fixed Point Theory and Applications
Year Published: 2019

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