On the convergence of iteration processes for semigroups of nonlinear mappings in banach spaces

Title: On the convergence of iteration processes for semigroups of nonlinear mappings in banach spaces
Creator: Kozlowski, W. M.; Sims, Brailey
Relation: Computational and Analytical Mathematics p. 463-484
Relation: Springer Proceedings in Mathematics & Statistics 50
Publisher Link: http://dx.doi.org/10.1007/978-1-4614-7621-4_22
Publisher: Springer
Resource Type: book chapter
Date: 2013
Description: Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the convergence of the generalized Krasnosel’skii-Mann and Ishikawa iteration processes to common fixed points of pointwise Lipschitzian semigroups of nonlinear mappings T t : C → C. Each of T t is assumed to be pointwise Lipschitzian, that is, there exists a family of functions α t : C → [0,∞) such that ∥Tt(x)−Tt(y)∥≤αt(x)∥x−y∥ for x,y ∈ C.
Subject: asymptotic pointwise nonexpansive mapping; common fixed point; semigroup of mappings; uniformly convex Banach space; primary 47H09; secondary 47H10; fixed-point; fixed point iteration process; Ishikawa process; Krasnosel’skii-Mann process; Lipschitzian mapping; Mann process; opial property; pointwise Lipschitzian mapping
Identifier: http://hdl.handle.net/1959.13/1066622
Identifier: uon:18175
Identifier: ISBN:9781461476214
Language: eng