Fixed point property and approximation of a class of nonexpansive mappings
Yisheng Song, Ying J. Huang · Fixed Point Theory and Applications · 2014
We introduce the concept of ψ -firmly nonexpansive mapping, which includes a firmly nonexpansive mapping as a special case in a uniformly convex Banach space. It is shown that every bounded closed convex subset of a reflexive Banach space has the fixed point property for ψ -firmly nonexpansive mappings, an important subclass of nonexpansive mappings. Furthermore, Picard iteration of this class of mappings weakly converges to a fixed point. MSC: 47H06, 47J05, 47J25, 47H10, 47H17.