Existence of fixed points for pairs of mappings and application to Urysohn integral equations

  • Deepak Kumar Lovely Professional University
  • Sumit Chandok Thapar University


In the present manuscript, we establish some results on common fixed point for two weakly compatible pairs of mappings in the setting of $C$-complex valued metric space. Also, as application of the proved result, we obtain the existence and uniqueness of a common solution of the system of the Urysohn integral equations:
where $i=1, 2, 3, 4, a, b\in \mathbb{R}$ with conditions $a\leq b, x, \psi_i\in C([a,b],\mathbb{R}^n), t\in [a,b]$ and $K_i:[a,b]\times [a,b]\times \mathbb{R}^n\rightarrow \mathbb{R}^n$ is a mapping for each $i=1, 2, 3, 4$.