Two fixed point results on b-metric space

In this paper, we present two fixed point theorems on $b$-metric spaces. First, we obtain a general result, which includes many fixed point theorems on $b$-metric space in the literature as a special case, by using implicit relation technique, Then, we define the concept of nearly Lipschitzian mapping in $b$-metric spaces, and we obtain a fixed point theorem for such mappings.