Fixed point iteration processes for asymptotic pointwise nonexpansive mapping in modular function spaces
1 Department of Mathematics, King Abdulaziz University, P.O. Box 53909, Jeddah, 21593, Saudi Arabia
2 School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia
Fixed Point Theory and Applications 2012, 2012:118 doi:10.1186/1687-1812-2012-118Published: 20 July 2012
Let be a uniformly convex modular function space with a strong Opial property. Let be an asymptotic pointwise nonexpansive mapping, where C is a ρ-a.e. compact convex subset of . In this paper, we prove that the generalized Mann and Ishikawa processes converge almost everywhere to a fixed point of T. In addition, we prove that if C is compact in the strong sense, then both processes converge strongly to a fixed point.
MSC: 47H09, 47H10.