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Common fixed points of generalized contractions on partial metric spaces and an application. (English) Zbl 1244.54090
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 [I. Altun, F. Sola and 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(·,0) has a fixed point iff H(·,1) has a fixed point.
54H25Fixed-point and coincidence theorems in topological spaces
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