Nonlinear Functional Analysis

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Viscosity approximation methods for nonexpansive mappings and monotone mappings (2007, unknown): “It is well known that PC satisfies 〈x − y,PCx − PCy〉 ‖PCx − PCy‖2 (1) for every x, y ∈ H , and PC is characterized by the following properties: 〈x − PCx,PCx − y〉 0, (2) ‖x − y‖2 ‖x − PCx‖2 + ‖y − PCx‖2 (3) for all x ∈ H , y ∈ C.”
Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings (2011, background): “Recall that a Banach space E has the Kadec-Klee property [15-17], if for any sequence {xn} ⊂ E and x Î E with xn ⇀ x and ||xn|| ® ||x||, then ||xn - x|| ® 0 as n ® ∞.”
On coincidence point and fixed point theorems for nonlinear multivalued maps (2012, background): “, [1]) which plays an important role in various fields of nonlinear analysis.”