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Fixed point theory for cyclic weak \(\phi\)-contraction. (English) Zbl 1256.54073
Appl. Math. Lett. 24, No. 6, 822-825 (2011); corrigendum ibid. 25, No. 10, 1582–1584 (2012).
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 M. Păcurar and I. A. Rus in [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3–4, A, 1181–1187 (2010; Zbl 1191.54042)].

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
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