Fixed points for generalized nonexpansive mappings
The purpose of this paper is to prove an existence result for a multivalued Cauchy problem using a fixed point theorem for a multivalued contraction on a generalized complete metric space.
It is proved that: for every Banach space which has uniformly normal structure there exists a with the property: if is a nonempty bounded closed convex subset of and is an asymptotically regular mapping such that where is the Lipschitz constant (norm) of , then has a fixed point in .
We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study the existence of fixed points and the structure of fixed point sets of mappings of these classes in Banach...