STRONG CONVERGENCE OF PATHS FOR NONEXPANSIVE SEMIGROUPS IN BANACH SPACES
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Abstract
Let E be a uniformly convex Banach space with a uni-
formly Gateaux differentiable norm, C be a nonempty closed convex
subset of E and f : C → C be a fixed bounded continuous strong
pseudocontraction with the coefficient α ∈ (0, 1). Let {λt }0<t<1
be a net of positive real numbers such that limt→0 λt = ∞ and
S = {T (s) : 0 ≤ s < ∞} be a nonexpansive semigroup on C such
that F (S) ̸= ∅, where F (S) denotes the set of fixed points of the
semigroup. Then sequence {xt } defined by
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