On the set of common fixed points of semigroups of nonlinear mappings in modular function spaces

被引：0
作者：
Saud M Alsulami
Walter M Kozlowski
机构：
[1] King Abdulaziz University,Department of Mathematics
[2] University of New South Wales,School of Mathematics and Statistics
来源：
Fixed Point Theory and Applications | / 2014卷
关键词：
fixed point; common fixed point; nonexpansive mapping; semigroup of nonlinear mappings; modular function space; Orlicz space; convex modular; fixed point iteration process; Mann process; Ishikawa process;
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摘要：
We prove that the set of all common fixed points for a continuous nonexpansive semigroup of nonlinear mappings acting in modular function spaces can be represented as an intersection of fixed points sets of two nonexpansive mappings. This representation is then used to prove convergence of several iterative methods for construction of common fixed points of semigroups of nonlinear mappings. We also demonstrate an example how the results of this paper can be applied for constructing a stationary point of a process defined by the Urysohn integral operator.
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