Fixed point theorems and tiling problems
Abstract
Let $(X, d)$ be a complete metric
space and let $f:X\to X$ satisfy $\inf\{\alpha(x, y)d(f^m(x),
f^m(y)): m\in\mathbb{J}\}\leq Kd(x, y)$ for all $x, y\in X$ and
some $K\in (0, 1)$ and $\alpha:X\times X\to [0, \infty)$, where
$\mathbb{J}$ is a set of positive integers. In this paper, we
prove fixed point theorems for this mapping $f$. We also discuss
the connection
with tiling problems and give a titling proof of a fixed point theorem.
space and let $f:X\to X$ satisfy $\inf\{\alpha(x, y)d(f^m(x),
f^m(y)): m\in\mathbb{J}\}\leq Kd(x, y)$ for all $x, y\in X$ and
some $K\in (0, 1)$ and $\alpha:X\times X\to [0, \infty)$, where
$\mathbb{J}$ is a set of positive integers. In this paper, we
prove fixed point theorems for this mapping $f$. We also discuss
the connection
with tiling problems and give a titling proof of a fixed point theorem.
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