Some Common Fixed-Point Theorem on Complex-Valued Metric Spaces and Its Application to Solve Urysohn Integral Equations

In this paper, a new and generalized contraction principles are proved on complex-valued metric space. By adopting a suitable hypothesis on sequence converging in complex-valued metric space new contractions are established for proving the common fixed-point theorem. Moreover, a rational contractive condition is improved in the complex-valued metric spaces. The obtained results through theoretical study are verified by solving the solution of the nonlinear system of Urysohn integral equations.