Fixed Point Theorems and Weak Convergence Theorems for Generalized Hybrid Mappings in Hilbert Spaces

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The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space (2018, background): “A mapping U : C → H is called generalized hybrid [6] if there exist α, β ∈ R such that α‖Ux− Uy‖(2) + (1− α)‖x− Uy‖(2) ≤ β‖Ux− y‖(2) + (1− β)‖x− y‖(2) for all x, y ∈ C.”
TWO GENERALIZED STRONG CONVERGENCE THEOREMS OF HALPERN’S TYPE IN HILBERT SPACES AND APPLICATIONS (2012, background): “In [11], they proved the following theorem which represents a relation between the class of generalized hybrid mappings and the class of extended hybrid mappings in a Hilbert space; see also [12] and [26].”