Explicit averaging cyclic algorithm for common fixed points of a finite family of asymptotically strictly pseudocontractive mappings in q-uniformly smooth Banach spaces
Ying Zhang, Zhiwei Xie · Fixed Point Theory and Applications · 2012
Let E be a real q -uniformly smooth Banach space which is also uniformly convex and K be a nonempty, closed and convex subset of E . We obtain a weak convergence theorem of the explicit averaging cyclic algorithm for a finite family of asymptotically strictly pseudocontractive mappings of K under suitable control conditions, and elicit a necessary and sufficient condition that guarantees strong convergence of an explicit averaging cyclic process to a common fixed point of a finite family of asymptotically strictly pseudocontractive mappings in q -uniformly smooth Banach spaces. The results of this paper are interesting extensions of those known results. MSC: 47H09, 47H10.