Saeed Shabani, S., Hoseini Ghoncheh, S. (2010). Approximating xed points of generalized non-expansive non-self mappings in CAT(0) spaces. Theory of Approximation and Applications, 7(1), 89-95.

Saeed Saeed Shabani; S. J. Hoseini Ghoncheh. "Approximating xed points of generalized non-expansive non-self mappings in CAT(0) spaces". Theory of Approximation and Applications, 7, 1, 2010, 89-95.

Saeed Shabani, S., Hoseini Ghoncheh, S. (2010). 'Approximating xed points of generalized non-expansive non-self mappings in CAT(0) spaces', Theory of Approximation and Applications, 7(1), pp. 89-95.

Saeed Shabani, S., Hoseini Ghoncheh, S. Approximating xed points of generalized non-expansive non-self mappings in CAT(0) spaces. Theory of Approximation and Applications, 2010; 7(1): 89-95.

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

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

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

Abstract

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 x_{1}ε K, x_{n+1} = P((1-α_{n})x_{n}+α_{n}TP[(1-α_{n})x_{n}+β_{n}Tx_{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.

Article Title [Persian]

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

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

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

Abstract [Persian]

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 x_{1}ε K, x_{n+1} = P((1-α_{n})x_{n}+α_{n}TP[(1-α_{n})x_{n}+β_{n}Tx_{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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