Abstract
We study the existence and uniqueness of coincidence point for nonlinear mappings of any number of arguments under a weak ()-contractivity condition in partial metric spaces. The results we obtain generalize, extend, and unify several classical and very recent related results in the literature in metric spaces (see Aydi et al. (2011), Berinde and Borcut (2011), Gnana Bhaskar and Lakshmikantham (2006), Berzig and Samet (2012), Borcut and Berinde (2012), Choudhury et al. (2011), Karapınar and Luong (2012), Lakshmikantham and Ćirić (2009), Luong and Thuan (2011), and Roldán et al. (2012)) and in partial metric spaces (see Shatanawi et al. (2012)).
Highlights
We study the existence and uniqueness of coincidence point for nonlinear mappings of any number of arguments under a weak (ψ, φ)-contractivity condition in partial metric spaces
The notion of coupled fixed point was introduced by Guo and Lakshmikantham [1] in 1987
Berinde and Borcut [7] introduced the concept of tripled fixed point and proved tripled fixed-point theorems using mixed monotone mappings
Summary
The notion of coupled fixed point was introduced by Guo and Lakshmikantham [1] in 1987. Gnana Bhaskar and Lakshmikantham [2] introduced the concept mixed monotone property for contractive operators of the form F : X × X → X, where X is a partially ordered metric space, and established some coupled fixed-point theorems. Roldan et al [11] proposed the notion of coincidence point between mappings in any number of variables and showed some existence and uniqueness theorems that extended the mentioned previous results for this kind of nonlinear mappings, not necessarily permuted or ordered, in the framework of partially ordered complete metric spaces, using a weaker contraction condition, that generalized other works by Berzig and Samet [12], Karapınar and Berinde [13]. We notice that our results cannot be obtained by the very recent paper of Haghi et al [21] (for more details see Remark 26)
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