Abstract
In this paper, we construct a deterministic fractal in fuzzy metric space using generalized fuzzy contraction mapping and its fixed-point theorem in hyperspace of non-empty compact sets. Moreover, we present the self-similar group of H-contraction in fuzzy metric space and prove some familiar results of self-similar group for fuzzy metric space.
Highlights
At the origin, fractal was defined by rough or fragmented geometric shape that can be split into parts where each smaller part is reduced size of the whole
On the basis of self-similar group of Banach contraction in classical metric space given by Saltan and Demir (2013), in this paper, we introduce the definition and property of self-similar group and strong self-similar group of -contraction
Second direction is that we investigate a fuzzy metric group on self-similar property of fractal set in order to define the topological group with generalized fuzzy contraction
Summary
Fractal was defined by rough or fragmented geometric shape that can be split into parts where each smaller part is reduced size of the whole. Fractal set can be defined as a self-similar and strong self-similar group in the sense of -IFS of compact topological space. Second direction is that we investigate a fuzzy metric group on self-similar property of fractal set in order to define the topological group with generalized fuzzy contraction.
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