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Iterative Methods for Contraction Operators in the Product of Two Metric Spaces
Author(s) -
Bassanini P.
Publication year - 1982
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19820620102
Subject(s) - lipschitz continuity , mathematics , metric space , contraction (grammar) , product metric , operator (biology) , metric (unit) , metric map , discrete mathematics , iterative method , product (mathematics) , constant (computer programming) , pure mathematics , convex metric space , mathematical optimization , computer science , geometry , medicine , biochemistry , chemistry , operations management , repressor , transcription factor , economics , gene , programming language
Abstract Let (S 1 , d 1 ), (S 2 , d 2 ) be (closed subsets of) complete metric spaces, (S, d̃) = (S 1 × S 2 , d̃) and let T: S → S, × = Tx be a Lipschitz continuous operator (strictly) contractive in S for a suitable choice of its Lipschitz constants and of d̃. Conditions are given under which there may exist iteration procedures whose expense of computer time is lower than required by the usual iterative scheme x n = Tx n−1 .