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Iterative Solutions of Nonlinear Equations of the Strongly Accretive Type
Author(s) -
Chidume C. E.
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981890105
Subject(s) - mathematics , banach space , fixed point , nonlinear system , type (biology) , fixed point iteration , iterative method , pure mathematics , domain (mathematical analysis) , mathematical analysis , space (punctuation) , iterative and incremental development , discrete mathematics , mathematical optimization , ecology , linguistics , physics , philosophy , software engineering , quantum mechanics , engineering , biology
Let E be a real q ‐uniformly smooth Banach space. Suppose T is a strongly pseudo‐contractive map with open domain D ( T ) in E. Suppose further that T has a fixed point in D(T). Under various continuity assumptions on T it is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provided.