Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces

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Generalized Projection Algorithms for Nonlinear Operators (2007, unknown): “‖Tx − Ty‖ ≤ ‖x − y‖, ∀x , y ∈ C , and relatively nonexpansive [4, 5, 7] if F̂ (T ) = F (T ) and (p,Tx) ≤ (p, x), ∀x ∈ C , p ∈ F (T )”
Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings (2011, background): “The asymptotic behavior of a relatively nonexpansive mapping was studied in [21-23].”
Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces (2008, background): “... points of T by F (T ), that is, F (T )= {z ∈ C : Tz = z}. A point u ∈ C is said to be an asymptotic fixed point (Reich [23]) of T if there exists a sequence {xn} of C such that xn �u and xn − Tx n → 0. We denote the set of asymptotic fixed points of T by F (T ). Following Matsushita and Takahash”