On generalized contraction in complex-valued metric spaces

The concept of complex-valued metric spaces has had a significant impact on research in fixed point theory. Although complex-valued metric spaces represent a distinct category of cone metric spaces, this concept aims to establish rational expressions that lack significance within cone metric spaces. Consequently, numerous analytical results cannot be extended to cone metric spaces. Along this direction, a common fixed point theorem satisfying a hybrid contraction, employing rational expression in the settings of complex-valued metric spaces is established. The results outlined enhance various fixed point theorems applicable to metric spaces as well as complex valued metric spaces.