Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces

This thesis examines and focuses on generalized non-expansive mappings, which are a new type of a class of non-expansive mappings. This new class of nonlinear mappings includes non-expansive mappings, a class of Suzuki-type generalized non-expansive mappings. In this thesis, the articles provided in the references section, are examined in details and the relations between α-non-expansive mappings and some other nonlinear mappings are studied. The fixed point approach of these mappings is studied by using Noor iteration process. In addition, the approximation of generalized α-non-expansive mappings to fixed points is studied by a new iteration process and examples of these fixed point approximations are provided.