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

Document Type: Research Articles


1 Department of Mathematics, Izeh Branch, Islamic Azad University, Izeh, Iran.

2 Department of Mathematics, Takestan Branch, Islamic Azad University, Takestan, Iran.


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 ε K : Tx = x}≠Φ.
Suppose fxng is generated iteratively by x1ε K, xn+1 = P((1- αn)xn+αnTP[(1- αn)xn+β nTxn]),n≥1, where {αn }and {βn } are real sequences in[ε,1-ε] for some  ε in (0,1). Then {xn} is Δ-􀀀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.

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