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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
##### Keywords:
cyclic weak $$\phi$$-contraction; fixed-point theory
Full Text:
##### References:
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