In this paper, we generalized the results presented in the paper W. Long, S. Khaleghizadeh, P. Salimi, S. Radenović and S. Shukla, \emph{Some new fixed point results in partially ordered metric spaces via admissible mappings,} Fixed Point Theory Appl. (2014), 2014:117, in the framework of partial metric spaces by using $C-$class function in ordered structure. Also, we provide an example to support our theoretical results and shows that obtained results are potential generalization of the already existing results in literature.