Coupled fixed point on ordered cone metric spaces with application in integral equations

Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone metric spaces in which linear contractive conditions appear‎, ‎can be reduced to their respective results in the metric setting‎, ‎but it has been shown in the papers [W‎. ‎S‎. ‎Du, New cone fixed point theorems for nonlinear multivalued maps with their applications‎, ‎Applied Mathematic Letters,‎24(2011) 172-178.] and [S‎. ‎Jankovic‎, ‎Z‎. ‎Kadelburg‎, ‎S‎. ‎Radenovic‎, ‎On cone metric spaces‎: ‎A survey‎, ‎Nonlinear Analysis‎, ‎74(2011) 2591-2601‎.] ‎when‎, cone metric spaces are non-normal‎, the results may not hold‎.The results from our paper belong to this category‎.