SECOND-ORDER DIFFERENTIAL PROXIMAL METHODS FOR EQUILIBRIUM PROBLEMS

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On the proximal point method for equilibrium problems in Hilbert spaces (2010, methodology): “Both in [16] and in [11] existence of the iterates is assumed as a hypothesis.”
Auxiliary Principle Technique for Equilibrium Problems (2004, methodology): “Let ˆ u be a cluster point of {un} and let the subsequence {unj } of the sequence {un} converge to ˆ u ∈ H . Replacing wn by unj in (12) and (13), taking the limit nj −→ ∞ , and using ( 25 ), we have”
Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space (2003, unknown): “In this direction, a straightforward adaptation (see, for instance, [19]) of the proof of [2, Thm.”
Equilibrium programming in Hilbert spaces (2005, background): “1) in this context in the case of a single bifunction (see [22, 23] and, in the case of Euclidean spaces, [13, 17, 20]), we are not aware of any result for systems of equilibrium problems.”