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This article is cited in 6 scientific papers (total in 6 papers)
Scientific articles
On coincidence points of mappings in generalized metric spaces
T. V. Zhukovskayaa, W. Merchelab, A. I. Shindyapinc a Tambov State Technical University
b Derzhavin Tambov State University
c Eduardo Mondlane University
Abstract:
Let $X$ be a space with $\infty$-metric $\rho$ (with possibly infinite value) and $Y$ a space with $\infty$-distance $d$ satisfying the identity axiom. We consider the problem of the coincidence point for the mappings $F,G:X \to Y$ of the existence of the solution for the equation
$F(x)=G(x).$ We provide conditions of the existence of the coincidence points in terms of the covering set for the mapping $F$ and the Lipschitz set for the mapping $G$ in the space $X\times Y.$ The $\alpha$-covering set
($\alpha > 0$) of the mapping $F$ — is the set of such $(x,y),$ that
$$\exists u\in X \ F(u)=y, \ \ \rho(x,u)\leq \alpha^{-1}d(F(x),y), \ \ \rho(x,u)<\infty,$$
and the $\beta$- Lipschitz set ($\beta\geq 0$) for the mapping $G$ — is the set of such $(x,y),$ that
$$ \forall u\in X\,\, G(u)=y \, \Rightarrow \, d(y,G(x))\leq \beta \rho(u,x).$$
The new results are compared with the known theorems about the coincidence points.
Keywords:
coincidence point of two mappings, metric, distance, covering mapping.
Received: 23.12.2019
Citation:
T. V. Zhukovskaya, W. Merchela, A. I. Shindyapin, “On coincidence points of mappings in generalized metric spaces”, Russian Universities Reports. Mathematics, 25:129 (2020), 18–24
Linking options:
https://www.mathnet.ru/eng/vtamu167 https://www.mathnet.ru/eng/vtamu/v25/i129/p18
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