Approximating fixed points of generalized non-expansive non-self mappings in CAT(0) spaces

Suppose K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T : K → X be a nonself mapping, satisfying condition (C) with F(T) := {x ∈ K : T x = x} 6= ∅. Suppose {xn} is generated iteratively by x1 ∈ K, xn+1 = P((1 − αn)xn ⊕ αnT P[(1 − βn)xn ⊕ βnT xn]),n ≥ 1, where {αn} and {βn} are real sequences in [, 1 − ] for some ∈ (0, 1). Then {xn} is ∆−convergence to some point x ∗ in F(T). This work extends a result of Laowang and Panyanak [5] to the case of generalized nonexpansive nonself mappings.