VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE MAPPINGS

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Convergence Theorem for Equilibrium Problems and Fixed Point Problems of Infinite Family of Nonexpansive Mappings (2007, background): “Let {xn} and {yn} be bounded sequences in a Banach space X and let {βn} be as equence in[0,1] with 0 10 ]).”
Mixed equilibrium problems and optimization problems (2009, neutral): “(See [24].”
Viscosity approximation methods for nonexpansive mappings and monotone mappings (2007, neutral): “(6) Setting p = q∗ in (5), we have 〈 q − f (q), q − q∗〉 0, (7) and setting p = q in (6), we obtain 〈 q∗ − f (q∗), q∗ − q〉 0.”
Solving variational inequalities involving nonexpansive type mappings (2008, positive): “1, Xu [24]) Let C be a nonempty closed convex subset of a uniformly smooth Banach space X, f ∈ ΠC and T : C → C a nonexpansive mapping with F (T ) 6= ∅.”
On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space (2015, methodology): “Since the mapping S is only non-expansive, it is necessary to apply some regularizing procedure, like the so-called viscosity approximation method, [21–24] to obtain the strong convergence of the method of successive approximations.”