Fixed point results under various contractive conditions in partial metric spaces (Q380413)

In Section 3 of this paper, the authors obtain fixed and common fixed point theorems for a selfmap and two selfmaps of a partial metric space satisfying some contraction type conditions. Theorem 3.1, the main result for a selfmap, is a special case of Theorem 4.1 in this paper, which is a particular case of a fixed point theorem of \textit{I. Altun} et al. [Topology Appl. 157, No. 18, 2778--2785 (2010; Zbl 1207.54052)] (cf. also Theorem 3 of \textit{S. Romaguera} [Topology Appl. 159, No. 1, 194--199 (2012; Zbl 1232.54039)]). Theorem 3.5, the main result for a common fixed point theorem of two selfmaps, is a particular case of Corollary 2.2 of \textit{L. Ćirić} et al. [Appl. Math. Comput. 218, No. 6, 2398--2406 (2011; Zbl 1244.54090)]. A weakly contractive version of Theorem 4.1 is obtained (cf. Theorem 5.1) and an example (Example 5.4) is given to justify the same. However, the selfmap considered in Example 5.1 is a Banach contraction, and so does not serve the purpose.