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

Theory of Approximation and Applications

مقاله 7، دوره 7، شماره 1، مرداد 2013، صفحه 89-95   

نوع مقاله: Research Articles

نویسندگان

Saeed Saeed Shabani^{* 1}؛ S. J. Hoseini Ghoncheh²

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

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

چکیده

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, 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
F(T). This work extends a result of Laowang and Panyanak [5] to the case of
generalized nonexpansive nonself mappings.

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