Unifying a multitude of common fixed point theorems with complex coefficients employing an implicit relation

Abstract

The concept of complex valued metric spaces was introduced and studied by Azam et al. (cf. [1]). Afterward, by mathematicians many fixed point theorems for mappings that satisfying in a rational inequality with real coefficients were founded in complex valued metric spaces. In this paper, we first, introduce implicit function with complex coefficient. Second, we establish common fixed point theorems involving two pairs of weakly compatible mapping satisfying certain rational expressions with complex coefficients are proved in complex valued metric space. Some related results are also derived besides furnishing illustrative examples to highlight the realized improvements. The presented theorems generalize, extend and improve many existing results in the literature.