More general contractions in perturbed metric spaces

In the present paper, we introduce two new types of contractive mappings in perturbed metric spaces, namely $\phi$-perturbed mappings and perturbed Kannan mappings. We prove a fixed point result for such mappings and show that our results are more general then the existing ones. We give an example to illustrate that our results are more general then the existing results and show that perturbed Kannan mappings are not necessarily continuous.