Fixed point theory for cyclic weak \(\phi\)-contraction (Q2430031)

The author discusses the existence of the fixed point of cyclic weak \(\phi\)-contraction mapping. He proved that a self-mapping \(T\) on a complete metric space \(X\) has a unique fixed point if it is cyclic weak \(\phi\)-contraction. The concept of cyclic weak \(\phi\)-contraction is introduced by \textit{M. Păcurar} and \textit{I. A. Rus} in [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3--4, A, 1181--1187 (2010; Zbl 1191.54042)].