- 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
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