Abstract
Let be N strictly pseudononspreading mappings defined on closed convex subset C of a real Hilbert space H. Consider the problem of finding a common fixed point of these mappings and introduce cyclic algorithms based on general viscosity iteration method for solving this problem. We will prove the strong convergence of these cyclic algorithm. Moreover, the common fixed point is the solution of the variational inequality .
Highlights
Throughout this paper, we always assume that C is a nonempty, closed, and convex subset of a real Hilbert space H
It is a simple matter to see that the operator F is μη − γL -strongly monotone over H, that is: Fx − Fy, x − y ≥ μη − γL x − y 2, ∀ x, y ∈ H × H
Let {αn} be a sequence in 0, min{1, 1/τ} satisfying the following conditions: 3.44 which equivalently solves the variational inequality problem 3.2
Summary
Throughout this paper, we always assume that C is a nonempty, closed, and convex subset of a real Hilbert space H. Bx − By, x − y ≥ α Bx − By 2, ∀x, y ∈ C, 1.3 for such a case, B is said to be α-inverse-strongly monotone, iv k-Lipschitz continuous if there exists a constant k ≥ 0 such that. 7, Acedo and Xu introduced an explicit iteration scheme called the followting cyclic algorithm for iterative approximation of common fixed points of {Ti}Ni 1 in Hilbert spaces. They define the sequence {xn} cyclically by x1 α0x0 1 − α0 T0x0; x2 α1x1 1 − α1 T1x1;. Motivated and inspired by Acedo and Xu 7 , we consider the following cyclic algorithm for finding a common element of the set of solutions of ki-strictly pseudononspreading mappings {Ti}Ni 1. The algorithm above can be rewritten as xn 1 αnγ f xn I − μαnB Tω n xn, 1.15 where Tω n circularly
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