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Proceedings of the American Mathematical Society, 1956 Suppose that space is metric. A chain is a finite collection of open sets d1, d2, * * * , dn such that di intersects dj if and only if I i-jj I 1. If the elements of a chain are of diameter less than a positive number e, that chain is said to be an e-chain.
Eldon Dyer
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On Tarski's fixed point theorem [PDF]
Proceedings of the American Mathematical Society, 2014 A concept of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive and predicative version of Tarski's fixed point theorem is obtained.Comment: Proc. Amer. Math.
Curi, Giovanni
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A Noncontractive Fixed Point Theorem [PDF]
Proceedings of the American Mathematical Society, 1970 The sequence Txn so constructed contains a subsequence TXnk which converges to some x X and which, by Ascoli's theorem [3], is equicontinuous. It follows in turn from (1) that the sequence Xnk is equicontinuous. To complete the proof it suffices to show xn,(t)-x(t) in B.
E. J. Pellicciaro
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On a fixed point theorem of Greguš [PDF]
International Journal of Mathematics and Mathematical Sciences, 1986 We consider two selfmaps T and I of a closed convex subset C of a Banach space X which are weakly commuting in X, i.e.‖TIx−ITx‖≤‖Ix−Tx‖ for any x in X,and satisfy the inequality‖Tx−Ty‖≤a‖Ix−Iy‖+(1−a)max{‖Tx−Ix‖,‖Ty−Iy‖}for all x, y in C, where ...
Brian Fisher, Salvatore Sessa
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On a fixed point theorem of Pathak [PDF]
International Journal of Mathematics and Mathematical Sciences, 1991 It is shown that the continuity of the mapping in Pathak's fixed point theorem for normed spaces is not necessary.
Brian Fisher
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A fixed-point theorem for mappings
Journal of Mathematical Analysis and Applications, 1968 Alexander Abian
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On Krasnoselskii's Cone Fixed Point Theorem
Fixed Point Theory and Applications, 2008 In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types.
Kwong ManKam
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Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1988 Let \(f\) be an orbitally continuous self-mapping of a complete metric space \((X,d)\). In this note, a fixed point theorem is proved for the mapping \(f\) satisfying contractive conditions which are combinations of various distances between distinct points \(x\), \(y\), \(fx\), and \(fy\) from \(X\).
M. R. Singh, A. K. Chatterjee
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Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1984 The authors' main result is the following: Let (X,d) be a complete metric space and \(f: X\to X\) a self-mapping. If for x,y\(\in X\) and \(p>0\) the inequality \[ d(T^{2p}x,T^{2p}y)\leq a_ 1d(T^ px,T^{2p}x)+a_ 2d(T^ py,T^{2p}y)+a_ 3d(T^ px,T^ py) \] with \(a_ 1,a_ 2,a_ 3\geq 0\) and \(a_ 1+a_ 2+a_ ...
M. D. Khan, M. S. Khan
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A short and constructive proof of Tarski’s fixed-point theorem [PDF]
, 2005 I give short and constructive proofs of Tarski’s fixed-point theorem, and of Zhou’s extension of Tarski’s fixed-point theorem to set-valued ...
Echenique, Federico
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