## 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.