Results 271 to 280 of about 1,132,756 (313)

A Remark on Contractive Mappings

Canadian Mathematical Bulletin, 1970
Much current research is concerned with the fixed points of contractive mappings (mappings which shrink distance in some manner) from a metric space into itself. In this remark we shall point out that most mappings treated in the literature are very special in the sense that all these mappings satisfy a condition which is rather severe: every periodic ...
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Periodic Points and Contractive Mappings

Canadian Mathematical Bulletin, 1974
Let X be a non-empty set and f:X→X. A point x ∈ X is (i) a fixed point off f(x)=x, and (ii) a periodic point of f iff there is a positive integer N such that fN(x)=x. Also a periodic orbit of f is the (finite) set {x, f(x), f2(x),…} where x is a periodic point of f.
Hsieh, Tsu-Teh, Tan, Kok-Keong
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A-properness of contractive and condensing maps

Nonlinear Analysis: Theory, Methods & Applications, 2002
The authors study \(A\)-properness of condensing perturbations of the identity and related maps in a possibly non-reflexive Banach space. An application to the strongly nonlinear differential equation \[ x''(t)+ f(t, x(x), x'(t),x''(t))\quad\text{on } [0,1], \] subject to Dirichlet boundary conditions, is given as well.
Lan, Kunquan, Webb, Jeffrey R. L.
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Contraction mappings

Proceedings of the Steklov Institute of Mathematics, 2010
The author considers some \(M\)-Fejér type mappings in \(n\)-dimensional Euclidean spaces and applications to solving problems in linear and convex programming.
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Contractive Mappings on Unbounded Sets

Set-Valued and Variational Analysis, 2017
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Reich, Simeon, Zaslavski, Alexander J.
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A Note on a Sequence of Contraction Mappings

Canadian Mathematical Bulletin, 1969
Let E be a metric space. A mapping T of the space E into itself is said to be a contraction if there exist s a number k, with 0 ≤ k < 1 such thatfor any two points x, y ∈ E. Every contraction mapping is continuous.
Singh, S. P., Russell, W.
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Iteration of Contractions and Analytic Maps

Journal of the London Mathematical Society, 1990
The Denjoy-Wolff theorem states that if f is an analytic map of the unit disc into itself, then the iterates \(f^ n\) converge to some point in the closure of the unit disc. Excluding Möbius maps, each f is a contraction with respect to the hyperbolic metric. The result is generalized to contractions of Hadamard and visibility n-dimensional manifolds.
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Contraction kernels and combinatorial maps

Pattern Recognition Letters, 2003
Summary: Graph pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids overcome the main limitations of their regular ancestors. The graphs used in the pyramid may be region adjacency graphs, dual graphs or combinatorial maps. Compared to usual graph data structures, combinatorial maps offer an explicit encoding
Luc Brun, Walter G. Kropatsch
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Extended Φ-contraction mappings

The Journal of Analysis
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Contraction Maps and Equivalent Linearization*

Bell System Technical Journal, 1967
This study is primarily concerned with the question: If the method of equivalent linearization indicates the existence of a periodic solution, is there actually a periodic solution near the approximation of equivalent linearization? To answer this question, we use a modification of the contraction mapping fixed point theorem. We discuss applications to
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