Two extensions of the Banach contraction mapping principle
نویسندگان
چکیده
منابع مشابه
The Banach contraction mapping principle and cohomology
By a dynamical system (X, T ) we mean the action of the semigroup (Z,+) on a metrizable topological space X induced by a continuous selfmap T : X → X. Let M(X) denote the set of all compatible metrics on the space X. Our main objective is to show that a selfmap T of a compact space X is a Banach contraction relative to some d1 ∈ M(X) if and only if there exists some d2 ∈ M(X) which, regarded as...
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These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in the theories of differential and integral equations and variational inequalities are given. Also discussed are Hilbert’s projective metric and iterated function systems
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We prove a type of converse of the Banach contraction mapping theorem for metric spaces: if X is a T 1 topological space and f : X ! X is a function with unique xed point a such that f n (x) converges to a for each x 2 X , then there exists a distance function d on X such that f is a contraction on the complete ultrametric space (X; d) with contractivity factor 1 2. We explore properties of the...
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*Correspondence: [email protected] 1Department of Mathematics, Çankaya University, Ankara, 06530, Turkey Full list of author information is available at the end of the article Abstract We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (I...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1968
ISSN: 0022-247X
DOI: 10.1016/0022-247x(68)90185-6