Abstract
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.
MSC:
Primary 47H09; secondary 46B20; 47H10; 47H20; 47E30; 47J25.