Generalized α-nonexpansive mappings in Banach spaces
Rahul Shukla, Rajendra Pant, Manuel De la Sen · Fixed Point Theory and Applications · 2017
Abstract We consider a new type of monotone nonexpansive mappings in an ordered Banach space X with partial order ⪯. This new class of nonlinear mappings properly contains nonexpansive, firmly-nonexpansive and Suzuki-type generalized nonexpansive mappings and partially extends α-nonexpansive mappings. We obtain some existence theorems and weak and strong convergence theorems for the Mann iteration. Some useful examples are presented to illustrate the facts.