Fixed points of cyclic weakly (\(\psi, \phi ,L, A, B\))-contractive mappings in ordered \(b\)-metric spaces with applications.

*(English)*Zbl 06334850Summary: We introduce the notion of ordered cyclic weakly (\(\psi, \phi ,L, A, B\))-contractive mappings, and we establish some fixed and common fixed point results for this class of mappings in complete ordered \(b\)-metric spaces. Our results extend several known results from the context of ordered metric spaces to the setting of ordered \(b\)-metric spaces. They are also cyclic variants of some very recent results in ordered \(b\)-metric spaces with even weaker contractive conditions. Some examples support our results and show that the obtained extensions are proper. Moreover, an application to integral equations is given here to illustrate the usability of the obtained results.

##### Keywords:

common fixed point; cyclic contraction; almost contraction; ordered \(b\)-metric space; altering distance function
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\textit{N. Hussain} et al., Fixed Point Theory Appl. 2013, Paper No. 256, 18 p. (2013; Zbl 06334850)

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