Modified viscosity type iteration for total asymptotically nonexpansive mappings in CAT(0) spaces and its application to optimization problems
Wiyada Kumam, Nuttapol Pakkaranang, Poom Kumam · The Journal of Nonlinear Sciences and Applications · 2017
In this paper, we introduce a modified two-step viscosity iteration process for total asymptotically nonexpansive mappings in CAT(0) spaces. We prove strong convergence of the proposed iteration process to a fixed point of total asymptotically nonexpansive mappings in CAT(0) spaces, which also shows that the limit of the sequence generated by proposed iteration process solves the solution of the variational inequality. We also provide illustrating a numerical example for supporting our main results. Moreover, we show the existence of solutions of our consequently results for some applications.