The purpose of this work is to prove some common xed point theorems for two operators on a set endowed with one or two vector-valued metrics. The use of vector-valued metrics makes it possible for each equation of a system to have its own Lipschitz property, while the use of two such metrics makes it possible for the Lipschitz condition to be expressed with respect to an incomplete metric. An application is presented for a system of operatorial equations.
The purpose of this paper is to prove common fixed point theorems for two operators without the assumption of continuity on a set endowed with vector-valued b-metric and we also study the case of two vector-valued b-metrics. The well-posedness of the fixed point problem is also discussed and an application is presented for systems of operator equations in complete b-normed vector space. Our results improve and generalize theorems 2 and 5 of M. Boriceanu [5].
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