1Department of Mathematics, Izeh Branch, Islamic Azad University, Izeh, Iran.
2Department of Mathematics, Takestan Branch, Islamic Azad University, Takestan, Iran.
عنوان مقاله [English]
Approximating xed points of generalized
non-expansive non-self mappings in CAT(0) spaces
نویسندگان [English]
Saeed Saeed Shabani1؛ 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 [English]
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.
کلیدواژه ها [English]
CAT(0) spaces, fi xed point, generalized non-expansive non-self mappings
مراجع
[1] M. Bridson and A. Hae iger, Metric Spaces of Non-Positive Curvature, vol. 319 of Fundamental Principles of Mathematical Sciences, Berlin, Germany, 1999. [2] S. Dhompongsa and W. Kirk and B. Sims, xed point of uniformly lipschitzian mappings, Nonlinear Anal. 65 (2006), 762{772. [3] S. Dhompongsa and B. Panyanak, On -convergence theorems in CAT(0) spaces. Computers and Mathematics with Applications. 56 (2008), 2572{2579. [4] W. Kirk and B. Panyanak, A concept of convergence in geodesic spaces. Nonlinear Anal. 68 (2008), 3689{3696. [5] W. Laowang and B. Panyanak, Approximating xed points of nonexpansive non- self mappings in CAT(0) spaces. Fixed Point Theory Appl. Article ID 367274 (2010), 11 pages. [6] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mapping, Math. Anal. Appl. 340 (2008), 1088{1095. [7] A. Razani and H. Salahifard, Invariant approximation for CAT(0) spaces, Non- linear Anal. 72 (2010), 2421{2425. [8] S. Dhompongsa, W. A. Kirk and B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear and Convex Anal. 8 (2007), 35-45.
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