Retraction method in fixed point theory for monotone nonexpansive mappings

In this paper we study the properties of the common fixed points set of a commuting family of monotone nonexpansive mappings in Banach spaces endowed with a graph. In particular, we prove that under certain conditions, this set is a monotone nonexpansive retract.

Convergence theorems of finite-step iteration with errors for non-self asymptotically nonexpansive in the intermediate sense mappings

Let K be a nonempty closed convex nonexpansive retract of a uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K ? E be non-self asymptotically nonexpansive in the intermediate sense mapping with F(T) = ?. Let {?ni}, {?ni} and {?ni} are sequences in [0, 1] with ?n(i) + ?n(i) + ?n(i) = 1 for all i = 1, 2, . . . , N. From arbitrary x1 ? K , define the sequence {xn } iteratively by (8), where {u(i) } for all i = 1, 2, . . . , N are bounded sequences in K with P? u(i) < ?. (i) If the dual E

Approximating common fixed points of finite family of asymptotically nonexpansive non-self mappings

Let K be a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1 , T2 , ... , TN : K ? E be N asymptotically nonexpansive nonself mappings with sequences {rin} such that ??(n=1) rin < ?, for all 1 ? i ? N and n n=1 n F = ?N(i-1) F (Ti) ? ?. Let {?in}, {?in} and {?in} are sequences in [0, 1] with i=1 ?in + ?in + ?in = 1 for all i = 1, 2, ... , N . From arbitrary x1 ? K , define the sequence {xn} iteratively by (6), where {uin} are bounded sequences in K with ??(n=1) uin < ?. (i) If the dual E*of E has the Kadec-Klee property, then {xn} converges weakly to a common fixed point x*? F ; (ii) if {T1 , T2 , ... , TN} satisfies condition (B), then {xn} converges strongly to a common fixed point x*? F. .