Abstract
In this paper, we show a Δ-convergence theorem for a Mann iteration procedure in a complete geodesic space with two quasinonexpansive and Δ-demiclosed mappings. The proposed method is different from known procedures with respect to the order of taking the convex combination.
Highlights
1 Introduction The fixed point approximation has been studied in a variety of ways and its results are useful for the other studies
{xn} -converges to a fixed point of T
Tn diverges and Further, in a CAT( ) space, Kimura et al [ ] proved the -convergence theorem for a family of nonexpansive mappings including the following scheme: xn+ = ( – αn)xn ⊕ αn ( – βn)Sxn ⊕ βnTxn
Summary
The fixed point approximation has been studied in a variety of ways and its results are useful for the other studies. In , Mann [ ] introduced an iteration procedure for approximating fixed points of a nonexpansive mapping T in a Hilbert space. Let C be a bounded closed convex subset of a complete CAT( ) space and T : C → C a nonexpansive mapping.
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