Fixed point results for mappings satisfying (ψ φ)-weakly contractive condition in ordered partial metric spaces

In [18], Matthews introduced a new class of metric spaces, that is, the concept of partial metric spaces, or equivalently, weightable quasi-metrics, are investigated to generalize metric spaces (X, d), to develop and to introduce a new fixed point theory. In partial metric spaces, the self-distance for any point need not be equal to zero. In this paper, we study some results for single map satisfying (ψ,φ)-weakly contractive condition in partial metric spaces endowed with partial order. An example is given to support the useability of our results.

Coincidence and fixed point results under generalized weakly contractive condition in partially ordered G-metric spaces

We deduce coincidence and fixed point theorems under generalized weakly contractive conditions in G-metric spaces equipped with partial order. We furnish examples to demonstrate the usage of the results and to distinguish them from the known ones.