Iterated Function System in ;-Metric Spaces

Abstract

Fractals have gained great attention from researchers due to their wide applications in engineering and applied sciences. Especially, in several topics of applied sciences, the iterated function systems theory has important roles. As is well known, examples of fractals are derived from the fixed point theory for suitable operators in spaces with complete or compact structures. In this article, a new generalization of Hausdorff distance h; on H(), H() is a class of all nonempty compact subsets of the generalized b-metric space (, d;). Completeness and compactness of (H() , h;) are analogously obtained from its counterparts of (, d;). Furthermore, a fractal is presented under a finite set of generalized μ-contraction mappings. Also, other special cases are presented.