Rotative mappings in Hilbert space (Q2708292)

A self-map \(T\) of a subset \(C\) of a Banach space \(X\) is called \((a,n)\)-rotative (\(n\in \mathbb{N}\), \(n\geq 2\), \(a\in [0,n)\)) if \(\|x- T^nx\|\leq a\|x-Tx\|\) for all \(x\in C\). In this paper the author studies the numerical Lipschitz constant for a fixed point free \((a,n)\)-rotative map in a Hilbert space. This corrects and extends some recent work of \textit{J. Górnicki} [Commentat. Math. Univ. Carol. 40, 495-510 (1999)].