Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

This paper studies the convergence of fixed points for Garsia-Falset generalized nonexpansive mappings. First, it investigates weak and strong convergence results for Garsia-Falset generalized nonexpansive mappings using the Temir-Korkut iteration in uniformly convex Banach spaces. This paper then exemplifies Garsia-Falset generalized nonexpansive mappings, which exceed the class of Suzuki generalized nonexpansive mappings. Moreover, it numerically compares this iteration's convergence speed with the well-known Thakur iteration of approximating the fixed point of Garsia-Falset generalized nonexpansive mapping. The results show that the Temir-Korkut iteration converges faster than the Thakur iteration converges. Finally, this paper discusses the need for further research.