Quasi contraction nonself mappings on Banach spaces and common fixed point theorems (Q2754944)

The main result of the paper is a common fixed point theorem for a function \(g\) defined on a closed convex subset \(C\) of a Banach space \(X\) mapping into \(X\) and a continuous function \(f:X\to X\) weakly commuting with \(g\) for which \(f(C) \subset C\) under a kind of quasi contraction assumption on \(g\). This extends a recent result of \textit{L. B. Ćirić} [Quasi contraction nonself mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts, Cl. Sci. Math. Natur. Sci. Math. 23, 25-31 (1998)] NEWLINENEWLINENEWLINEUsing the method of the proof of the main result, the author recovers some results of \textit{K. M. Das} and \textit{K.V. Naik} [Proc. Am. Math. Soc. 77, 369-373 (1979; Zbl 0418.54025)] and \textit{G. Jungck} [Am. Math.Monthly 83, 261-263 (1970; Zbl 0321.54025)] concerning the existence of a unique fixed point of commuting selfmaps of complete metric spaces one of them being quasi contractive in a sense.