Abstract:
The existence of fixed points of single-valued mappings in modular function spaces
has been studied by many authors. The approximation of fixed points in such spaces
via convergence of an iterative process for single-valued mappings has also been
attempted very recently by Dehaish and Kozlowski (Fixed Point Theory Appl.
2012:118, 2012). In this paper, we initiate the study of approximating fixed points by
the convergence of a Mann iterative process applied on multivalued ρ-nonexpansive
mappings in modular function spaces. Our results also generalize the corresponding
results of (Dehaish and Kozlowski in Fixed Point Theory Appl. 2012:118, 2012) to the
case of multivalued mappings.
