Geodesic
One estimate of fixed points and coincidence points of mappings of metric spaces
Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1255-1260 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{VTAMU_2017_22_6_a4,
     author = {M. V. Borzova and E. S. Zhukovskiy and N. Yu. Chernikova},
     title = {One estimate of fixed points and coincidence points of mappings of metric spaces},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {1255--1260},
     year = {2017},
     volume = {22},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a4/}
}
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M. V. Borzova; E. S. Zhukovskiy; N. Yu. Chernikova. One estimate of fixed points and coincidence points of mappings of metric spaces. Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1255-1260. http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a4/