Some results for the maps with a nonunique fixed point (Q1058186)

The author establishes some nonunique fixed point theorems for an orbitally continuous mapping \(T: M\to M\), M a T-orbitally complete metric space, satisfying the Ćirić type conditions [cf. \textit{L. B. Ćirić}, Publ. Inst. Math., Nouv. Sér. 17(31), 52-58 (1974; Zbl 0309.54035)]: \[ \min \{d(Tx,Ty),d(x,Tx),d(y,Ty)\}+a\cdot \min \{d(x,Ty),d(y,Ty)\}\leq p\cdot d(x,y)+q\cdot d(x,Tx) \] for all x,y\(\in M\) and a, p and q are real numbers such that \(0<p+q<1\). These results generalize some important results of \textit{S. Banach} [Fundam. Math. 3, 133-181 (1922)] and \textit{R. Kannan} [Am. Math. Monthly 76, 405-408 (1969; Zbl 0179.282).] An example is given.