An Extension of Some Common Fixed Point Theorems in Complex-Valued Metric Spaces

As a generalization of the ordinary metric spaces, complex-valued metric spaces have significantly influenced research in fixed point theory. The idea intends to develop rational expressions that are insignificant within the context of cone metric spaces since the latter banks on the underlying Banach space which is not a division ring. This paper demonstrates a common fixed point theorem applicable to a pair of mappings that fulfill a rational type contractive condition in the setting of complex-valued metric spaces. The mappings examined in this study are expected to comply with particular metric inequalities, which broadens and includes various results from other scholars that were established for mappings in complex-valued metric spaces.