Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces

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Equilibrium programming in Hilbert spaces (2005, background): “Remark 4.4 Consider the setting of Lemma 2.15(i) with K = H. Then, for every n 2 N, J nF = (Id+ nA) 1 and Theorem 4.3 therefore corresponds to [ 18, Theorem 1 ].”
Solving variational inequalities involving nonexpansive type mappings (2008, unknown): “Recently, Benavides, Acedo and Xu [2], Kamimura and Takahashi [8], Kim and Xu [9], Mainge [13], Nakajo [17] and Solodov and Svaiter [21] modified proximal point algorithm to generate strongly convergent sequences.”
A strong convergence theorem for relatively nonexpansive mappings in a Banach space (2005, background): “On the other hand, Kamimura and Takahashi [4] considered an algorithm to generate a strong convergent sequence in a Hilbert space.”
Weak and Strong Convergence Theorems for Maximal Monotone Operators in a Banach Space (2004, background): “Kamimura and Takahashi [ 8 ] also obtained the following strong convergence theorem:”
Monotone and Accretive Vector Fields on Riemannian Manifolds (2010, methodology): “In the setting of Banach spaces, iterative methods to approximate singularities of strongly monotone vector fields or, equivalently, fixed points of α-strongly pseudo-contractive mappings have been studied by many authors; see, for instance, [31, 32, 33].”