Ji, Youqing; Ri, Songil Certain fixed point theorems and applications to the fractal space. (English) Zbl 1340.37028 Commun. Math. Res. 31, No. 2, 180-192 (2015). 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 Keywords:fixed point; generalized contraction; Hausdorff distance; fractal; topological equivalence PDFBibTeX XMLCite \textit{Y. Ji} and \textit{S. Ri}, Commun. Math. Res. 31, No. 2, 180--192 (2015; Zbl 1340.37028) Full Text: DOI