Convergence theorems for modified generalized f-projections and generalized nonexpansive mappings
Qingqing Cheng, Yongfu Su, Jingling Zhang · Journal of Inequalities and Applications · 2014
Abstract The purpose of this paper is to study a sequence of modified generalized f-projections in a reflexive, smooth, and strictly convex Banach space and show that Mosco convergence of their ranges implies their pointwise convergence to the generalized f-projection onto the limit set. Furthermore, we prove a strong convergence theorem for a countable family of α-nonexpansive mappings in a uniformly convex and smooth Banach space using the properties of a modified generalized f-projection operator. Our main results generalize the results of Ziming Wang, Yongfu Su, and Jinlong Kang and enrich the research contents of α-nonexpansive mappings. MSC:47H05, 47H09, 47H10.