A Fixed Point Result in Fuzzy Metric Space with Application in Fractal Generation

In this paper, we construct an Iterated Function System (IFS) on a fuzzy metric space for generating fractal sets in that fuzzy metric space. A new cyclic contraction mapping is defined and utilized in the construction of the IFS. It is shown that the cyclic contraction has a unique fixed point when the space is complete. These contractions automatically do not possess continuity property. A fuzzy variant of the Hausdorff metric is used on the set of compact subsets of the fuzzy metric space. Two illustrative examples are discussed. Further, the fixed point theorem obtained here effectively generalizes a recent result in the literature.