Certain Fixed Point Theorems and Application to the Fractal Space (Communications in Mathematical Research, 2021)
In this paper, we present some important generalizations of the Banachcontraction principle, in which the Lipschitz constant $k$ is replaced by some real-valued control function. For the applications to the fractal space, we obtain the fixedpoint theorem of the some generalized contraction in the space of fractals.
Keywords: fixed point; generalized contraction; Hausdorff distance; fractal; topological equivalence.