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On coincidence points of mappings in generalized metric spaces


Let X be a space with ∞-metric ρ (a metric with possibly infinite value) and Y a space with ∞-distance d satisfying the identity axiom. We consider the problem of coincidence point for mappings F,G:X→Y, i.e. the problem of existence of a solution for the equation F(x)=G(x). We provide conditions of the existence of coincidence points in terms of a covering set for the mapping F and a Lipschitz set for the mapping G in the space X×Y. An α-covering set (α>0) of the mapping F is a set of (x,y) such that ∃u∈X F(u)=y, ρ(x,u)≤α^(-1) d(F(x),y), ρ(x,u)<∞, and a β - Lipschitz set (β≥0) for the mapping G is a set of (x,y) such that ∀u∈X G(u)=y⇒d(y,G(x))≤βρ(u,x). The new results are compared with the known theorems about coincidence points.


coincidence point of two mappings; metric; distance; covering mapping

Full-text in one file





517.988.6, 515.124.2




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