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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 k < 1 s 2 . 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. [ABSTRACT FROM AUTHOR]