The purpose of this paper is to obtain the common  xed point results for two pair of weakly compatible mapping by using common (CLR) property in partial metric space. Also we extend the very recent results which are presented in [19] with proo ng a new version of the continuity of partial metric.

The target of this paper is to present partial fuzzy metric-preserving functions and characterize the functions $f:[0,1]\to[0,1]$ with this aspect. We give a characterization for partial fuzzy  metric-preserving functions considering the different t-norms. Also, we show that the topology induced by partial fuzzy metric does not preserve under these functions with  an example. Then we  give a characterization of those partial fuzzy metric-preserving functions which preserve completeness and contractivity under some conditions. Finally, we discussed the relation between fuzzy  metric preserving and partial fuzzy preserving functions.

Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data ow networks. In 2014 Asadi and et al. [New Extension of p-Metric Spaces with Some  xed point Results on M-metric paces, J. Ineq. Appl. 2014 (2014): 18] extend the Partial metric spaces to M-metric spaces. In this work, we introduce the class of F(; ')-contractions and investigate the existence and uniqueness of  xed points for the new class C in the setting of M-metric spaces. The theorems that we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions.