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

Subject Areas : Applied Mathematics

Saeed Saeed Shabani ¹ , S.J. Hoseini Ghoncheh ²

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

Received: 2015-09-30 Accepted : 2015-09-30 Published : 2013-05-01

Keywords: fixed point, CAT(0) spaces, generalized non-expansive non-self mappings,

Abstract :

Suppose K is a nonempty closed convex subset of a complete CAT(0) spaceX with the nearest point projection P from X onto K. Let T : K →X be anonself mapping, satisfying condition (C) with F(T) :={ x εK : Tx = x}≠Φ.Suppose fxng is generated iteratively by x1εK, 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* inF(T). This work extends a result of Laowang and Panyanak [5] to the case ofgeneralized nonexpansive nonself mappings.

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