Abstract:
For single-valued and multi-valued mappings acting in a metric space $X$ and satisfying the Lipschitz condition, we propose a lower estimate of the distance from a given element $x_0\in X$ to a fixed point. Thus, we find $r>0$ such that there are no fixed points in the ball with center at $x_0$ of radius $r.$ The proof follows directly from the triangle inequality. The result is extended to $(q_1, q_2)$- metric spaces. An analogous estimate is obtained for coincidence points of covering and Lipschitz mappings of metric spaces.
Keywords:fixed point, point of coincidence, metric space, Banach theorem, Nadler’s theorem, lower estimate of the distance from a given element to a fixed point.
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