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ANALYSIS ON FRACTALS IN FUZZY METRIC SPACES

Department of Mathematics, The Gandhigram Rural Institute — Deemed University, Gandhigram — 624 302, Dindigul, Tamil Nadu, India

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R. UTHAYAKUMAR

Department of Mathematics, The Gandhigram Rural Institute — Deemed University, Gandhigram — 624 302, Dindigul, Tamil Nadu, India

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https://doi.org/10.1142/S0218348X11005543Cited by:31 (Source: Crossref)

Abstract

In this paper, we investigate the fractals generated by the iterated function system of fuzzy contractions in the fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard fuzzy metric spaces by using the fuzzy Banach contraction theorem. In addition to that, we discuss some results on fuzzy fractals such as Collage Theorem and Falling Leaves Theorem in the standard fuzzy metric spaces with respect to the standard Hausdorff fuzzy metrics.

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