Greguš, Michal A fixed point theorem in Banach space. (English) Zbl 0538.47035 Boll. Unione Mat. Ital., V. Ser. A 17, 193-198 (1980). Summary: A proof of the following theorem is given: Let C be a closed convex subset of a Banach space and let T:\(C\to C\) satisfy the condition \(\| Tx-Ty\| \leq a\| x-y\| +b\| Tx-x\| +c\| Ty-y\|\) with \(a+b+c=1\). Then T has a fixed point. Cited in 14 ReviewsCited in 29 Documents MSC: 47H10 Fixed-point theorems PDFBibTeX XMLCite \textit{M. Greguš}, Boll. Unione Mat. Ital., V. Ser., A 17, 193--198 (1980; Zbl 0538.47035)