Strong convergence of Halpern method for firmly type nonexpansive mappings
Yonghong Yao, Mihai Postolache, Naseer Shahzad · The Journal of Nonlinear Sciences and Applications · 2017
In this paper, Halpern method is applied to find fixed points of a class of firmly type nonexpansive mappings. A strong convergence result is obtained under the control conditions (C1) and (C2). Our conclusion obtained in this paper gives the affirmative answer of the Halpern open problem for this class of mapping.