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Zbl 1244.54090
Ćirić, Ljubomir; Samet, Bessem; Aydi, Hassen; Vetro, Calogero
Common fixed points of generalized contractions on partial metric spaces and an application.
(English)
[J] Appl. Math. Comput. 218, No. 6, 2398-2406 (2011). ISSN 0096-3003

The authors develop the fixed point theory on partial metric spaces and give some common fixed point theorems for four mappings satisfying the Ćirić type contraction condition. The main result (Theorem 2.1) generalizes the one proved quite recently in [{\it I. Altun, F. Sola} and {\it H. Simsek}, Topology Appl. 157, No. 18, 2778--2785 (2010); corrigendum ibid. 158, No. 13, 1738--1740 (2011; Zbl 1207.54052)]. At the end of the paper some homotopy results are presented. Under suitable assumptions on a homotopy $H$ (contractivity and continuity type conditions) the authors prove that $H(\cdot,0)$ has a fixed point iff $H(\cdot,1)$ has a fixed point.
[Grzegorz Gabor (Toruń)]
MSC 2000:
*54H25 Fixed-point theorems in topological spaces

Keywords: coincidence point; common fixed point; partial metric space; weakly compatible pair of maps; homotopy

Citations: Zbl 1207.54052

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