Volume 44_1-2_(2023)_27-51

Strong convergence theorems by Martinez-Yanes–-Xu projection method for mean-demiclosed mappings in Hilbert spaces
Atsumasa Kondo

Abstract. Strong convergence theorems that approximate common fixed points of two nonlinear mappings are presented. Our method is based on the Martinez-Yanes–-Xu iteration, which extends Nakajo and Takahashi's CQ method. In this paper, by exploiting the mean-valued iteration procedure, we further develop Nakajo and Takahashi's CQ method and Takahashi, Takeuchi, and Kubota's shrinking projection method. The approach of this paper does not require that the two mappings be continuous or commutative. The types of mappings considered in this paper include nonexpansive mappings and other well-known classes of mappings as special cases

Rend. Mat. Appl. (7) 44 (2023) 27-51;  pdf