FIXED POINT THEOREMS FOR NEW NONLINEAR MAPPINGS IN A HILBERT SPACE

By Wataru Takahashi, M. Ku, Natl Sun. 2010

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Fixed Point Theorems and Weak Convergence Theorems for Generalized Hybrid Mappings in Hilbert Spaces (2010, background): “Recently, Kohsaka and Takahashi [11], and Takahashi [16] introduced the following nonlinear mappings which are deduced from a firmly nonexpansive mapping in a Hilbert space.”
Fixed Point Theorems and Ergodic Theorems for Nonlinear Mappings in Hilbert Spaces (2011, unknown): “Then, from [16], we have the following equality: (3) ‖Tx− Ty‖2 = ‖x− y − (Tx− Ty)‖2 − ‖x− y‖2 + 2〈x− y, Tx− Ty〉 for all x, y ∈ C.”
Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces (2019, background): “As a consequence, various single-valued and multi-valued self and nonself mappings related to nonexpansive mappings were introduced and studied independently of in connection to nonexpansive mappings (see MathScinet or zbMATH): quasi-nonexpansive mappings (see [40]), strictly quasi-nonexpansive mapp”
The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space (2018, unknown): “It is also hybrid [15] for α = 3 2 and β = 1 2 , i.”