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Zbl 1200.47078
Takahashi, Wataru
Fixed point theorems for new nonlinear mappings in a Hilbert space. (English)
[J] J. Nonlinear Convex Anal. 11, No. 1, 79-88 (2010). ISSN 1345-4773; ISSN 1880-5221/e

Let $C$ be a closed convex subset of a Hilbert space $H;$ a mapping $T: C \to H$ satisfying $$ \|Tx - Ty\|^2 \leq \|x-y\|^2 +\langle x - Tx,y - Ty\rangle\quad \forall x,y \in C $$ is called hybrid. The author studies properties of hybrid mappings and proves some new fixed point theorems for them.
[Valerii V. Obukhovskij (Voronezh)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H09 Mappings defined by "shrinking" properties

Keywords: nonexpansive map; hybrid map; fixed point; Hilbert space; nonspreading mapping; equilibrium problem

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