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Fixed point theorems for new nonlinear mappings in a Hilbert space. (English) Zbl 1200.47078
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.

MSC:
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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