We establish a new fixed point theorem in the setting of convex b-metric spaces that ensures the existence of fixed point for Cirić contraction with the assumption k1s2. Also, the fixed point is approximated by Krasnoselskij iterative procedure. Moreover, we discuss the stability of fixed point for the aforesaid contraction. As a consequence, we develop a common fixed point and coincidence point result. Finally, we provide a number of examples to illustrate the findings presented here and incorporate these findings to solve an initial value problem.
