Corvergence theorems for a class of generalized nonexpansive mappings

In this thesis, the convergence results of fixed points for generalized nonexpansive mappings, referred to as Garcia-Falset generalized nonexpansive mappings, are studied. Using the T.S- iteration process, the convergence of Garcia-Falset generalized nonexpansive mappings to a fixed point is proven, and the fixed point approximations of these mappings are showed with examples. Additionally, it is shown that the Garcia-Falset generalized nonexpansive mapping encompasses the class of Suzuki-type generalized nonexpansive mappings and generalized α-nonexpansive mappings. With the given examples, the convergence of the T.S- iteration process used for approximating the fixed point of the Garcia-Falset generalized mapping is compared with other well-known iteration processes, and it is observed that the T.S. iteration process converges to the fixed point faster than the others.