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Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces. (English) Zbl 1181.47074
The author considers a uniformly convex Banach space E satisfying the Opial condition, a closed, convex subset C of E, and a Lipschitzian pseudo-contractive semigroup T:={T(t):t0}:CC such that F:= t0 F(T(t)), where F(T(t)) denotes the set of fixed points of T(t). Let (α n ) n be a sequence in (0,1) and (t n ) n a sequence in (0,) satisfying (i) lim sup n α n <1 and (ii) lim n t n =lim n α n t n =0. Under these circumstances, he shows that the sequence x 0 C, x n =α n x n-1 +(1-α n )T(t n )x n ,n1, is weakly convergent to a common fixed point of the semigroup.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H05Monotone operators (with respect to duality) and generalizations
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H20Semigroups of nonlinear operators
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