According to the relaxed method, an appropriate dither is introduced to steer the chaotic motion into a periodic orbit or a steady state.
Based on the extragradient method and viscosity approximation method, Yao et al. [8] proposed and analyzed a relaxed extragradient method for finding a common solution of GSVI (1.3) and a fixed point problem of a strictly pseudo-contractive mapping S : C → C. Theorem YLK (see [[8], Theorem 3.2]).
So, the algorithm in [11] can be considered as a relaxed SIU method.
In 2012, Dong et al. [6] proved strong convergence theorem by using a relaxed extragradient method as follows.
Precisely, they introduced a relaxed extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of variational inequality problem (4.5) in a real Hilbert space.
In particular, if the mapping A i : C → H is α ^ i -inverse strongly monotone for i = 1, 2, then the mapping G is nonexpansive provided λ i ∈ ( 0, 2 α ^ i ) fori = 1, 2. Utilizing Lemma 1.1, they proposed and analyzed a relaxed extragradient method for solving problem (1.2).
Approximate divergence times were estimated using a relaxed clock method [ 70] as implemented in BEAST 1.5.3 [ 71].
The purpose of this paper to study and analyze an relaxed extragradient method with regularization for finding a common element of the solution set Γ of the SFP and the set solutions of fixed points for asymptotically quasi-nonexpansive mappings and a Lipschitz continuous mapping in a real Hilbert space.
His astonishingly precise yet relaxed method has the decisive spontaneity of drypoint etchings; his depiction of emotional bewilderment is the source of a bracing artistic clarity.
Based on the relaxed method, the NDSP system can be stabilized by regulating appropriately the parameters of dither.
Based on the relaxed method, the NMTD system can be stabilized by regulating appropriately the parameters of dither.
