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

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In this paper, we establish some common fixed point results for two pairs of weakly compatible 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: eqnarray* x(t)=ψᵢ(t)+∫ₐᵇKᵢ(t,s,x(s))ds eqnarray* where i=1, 2, 3, 4, a,b∈ R with a≤ b, t∈ [a,b], x, ψᵢ∈ C([a,b],Rⁿ) and Kᵢ:[a,b]× [a,b]× Rⁿ→ Rⁿ is a mapping for each i=1, 2, 3, 4.