\(K\)-metric and \(K\)-normed linear spaces: Survey. (English) Zbl 0892.46002

We give a short survey on some fixed point theorems which are generalizations of the classical Banach-Caccioppoli principle for contractive mappings. All these results are gathered in three theorems about existence and uniqueness of fixed points for operators which act in \(K\)-metric or \(K\)-normed linear spaces and, in particular, in locally convex spaces and scales of Banach spaces. Three fixed point theorems presented in this article cover numerous applications to numerical methods, theory of integral equations, some results on iterative methods for construction of periodic solution to ordinary differential equations, existence and uniqueness results on the solvability of the Cauchy problem and Goursat problems of Ovsjannikov-Treves-Nirenberg type and others.


46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
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