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

Abstract

Suppose K is a nonempty closed convex subset of a complete CAT(0) space<br />X with the nearest point projection P from X onto K. Let T : K → X be a<br />nonself mapping, satisfying condition (C) with F(T) :={ x ε K : Tx = x}≠Φ.<br />Suppose fxng is generated iteratively by x₁ε K, x_n+1 = P((1- α_n)x_n +α_nTP[(1- α_n)x_n+β _nTx_n]),n≥1, where {α_n }and {β_n } are real sequences in[ε ,1-ε ] for some ε in (0,1). Then {x_n} is Δ- 􀀀convergence to some point x* in<br />F(T). This work extends a result of Laowang and Panyanak [5] to the case of<br />generalized nonexpansive nonself mappings.