Research Article Iteration Scheme with Perturbed Mapping for Common Fixed Points of a Finite Family of Nonexpansive Mappings
نویسندگان
چکیده
Let {Ti}i=1 be a finite family of nonexpansive self-maps of H . Denote the common fixed points set of {Ti}i=1 by ⋂N i=1 Fix(Ti). Let F : H → H be a mapping such that for some constants k,η > 0, F is k-Lipschitzian and η-strongly monotone. Let {αn}n=1 ⊂ (0,1), {λn}n=1 ⊂ [0,1) and take a fixed number μ ∈ (0,2η/k2). The iterative schemes concerning nonlinear operators have been studied extensively by many authors, you may refer to [1–12]. Especially, in [13], Zeng and Yao introduced the following implicit iteration process with perturbed mapping F. For an arbitrary initial point x0 ∈H , the sequence {xn}n=1 is generated as follows: xn = αnxn−1 + ( 1−αn )[ Tnxn− λnμF ( Tnxn )] , n≥ 1, (1.2)
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