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Certain fixed point theorems and applications to the fractal space. (English) Zbl 1340.37028

Summary: In this paper, we present some important generalizations of the Banach contraction principle, in which the Lipschitz constant \(k\) is replaced by some real-valued control functions. For the applications to the fractal space, we obtain the fixed point theorems of the some generalized contractions in the space of fractals.

MSC:

37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
28A80 Fractals
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
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