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Self-similar random fractal measures were studied by Hutchinson and Rüschendorf. Working with probability metric in complete metric spaces, they need the first moment condition for the existence and uniqueness of these measures. In this paper, we use contraction method in probabilistic metric spaces to prove the existence and uniqueness of self-similar random fractal measures replacing the first moment condition

The purpose of this paper is to present fixed point, strict fixed point and fixed set results for (singlevalued and multivalued) generalized contractions ofĆirić type. The connections between fixed point theory and the theory of self-similar sets is also discussed.

"Barnsley introduced in [1] the notion of fractal interpolation function (FIF). He said that a fractal function is a (FIF) if it possess some interpolation properties. It has the advantage that it can be also combined with the classical methods or real data interpolation. Hutchinson and Ruschendorf [7] gave the stochastic version of fractal interpolation function. In order to obtain fractal interpolation functions with more exibility, Wang and Yu [9] used instead of a constant scaling parameter a variable vertical scaling factor. Also the notion of fractal interpolation can be generalized to the graph-directed case introduced by Deniz and  Ozdemir in [5]. In this paper we study the case of a stochastic fractal interpolation function with graph-directed fractal function."

The aim of this paper is to present fixed set theorems, collage type and anticollage type results for single-valued operators T : X ×X → X in the framework of a complete metric space X. Based on the coupled fixed point theory, existence of fixed sets, collage type and anticollage type results for iterated function systems are also presented. The results are closely related to self-similar sets theory and the mathematics of fractals. Several examples of coupled fractals illustrate our results.