Rotative mappings in metric fixed point theory (Q2753306)

A nonexpansive selfmap \(T\) of a closed convex subset \(C\) in a Banach space \(X\) is called rotative if \(\|T^n x- x\|\leq a\|Tx- x\|\) \((x\in G)\) for some \(n\in\mathbb{N}\) and \(a<n\). Some papers dealing with fixed point and related theorems for rotative maps are due to both authors [Can. Math. Bull. 24, 113-115 (1981; Zbl 0461.47027) and Rend. Semin. Mat. Fis. Milano 51, 145-156 (1981; Zbl 0535.47031)], the second author [Boll. Unione Mat. Ital., VI. Ser., C, Anal. Funz. Appl. 5, 321-339 (1986; Zbl 0634.47053)], \textit{A. T. Plant} and \textit{S. Reich} [Proc. Japan Acad., Ser. A 58, 398-401 (1982; Zbl 0531.47056)], and \textit{S. Park} and \textit{S. Yie} [Bull. Korean Math. Soc. 23, 155-160 (1986; Zbl 0621.47052)]. In this paper the authors give a brief survey of what is known so far on this class of maps, including some open problems.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00060].