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Attracting Mappings in Banach and Hyperbolic Spaces

✍ Scribed by Simeon Reich; Alexander J. Zaslavski

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
133 KB
Volume
253
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we study spaces of mappings A : K Βͺ K satisfying Ax s x for all x g F, where K is a closed convex subset of a hyperbolic complete metric space and F is a closed convex subset of K. These spaces are equipped with natural Ε½ . complete uniform structures. We study the convergence of powers of F -attracting Ε½ . mappings as well as the convergence of infinite products of uniformly F -attract-Ε½ . ing sequences and show that if there exists an F -attracting mapping, then a Ε½ . generic mapping is also F -attracting. We also consider a finite sequence of subsets F ; K, i s 1, . . . , n, with a nonempty intersection F and a certain regulari Ε½ . ity property and show that if each mapping A is F -attracting, i s 1, . . . , n, then i i Ε½ . their product and convex combinations are F -attracting.

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