Mann iteration process for monotone nonexpansive mappings with a graph
Keyword(s):
Abstract Let {(X,\lVert\,\cdot\,\rVert)} be a Banach space. Let C be a nonempty, bounded, closed and convex subset of X and let {T:C\rightarrow C} be a G-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by x_{n+1}=t_{n}T(x_{n})+(1-t_{n})x_{n},\quad n=1,2,\dots, proves the existence of a fixed point of G-monotone nonexpansive mappings.
2005 ◽
Vol 2005
(11)
◽
pp. 1685-1692
◽
1994 ◽
Vol 124
(1)
◽
pp. 23-31