Rational type compatible single-valued mappings via unique common fixed point findings in complex-valued b-metric spaces with an application (Q2046636)

Summary: In this paper, we establish some new generalized rational type common fixed point results for compatible three self-mappings in complex-valued b-metric space, in which a one self-map is continuous. In support of our results, we present some illustrative examples to verify the validity of our main work. Moreover, we present the application of two Urysohn integral type equations (UITEs) for the existence of a common solution to support our work. The UITEs are \(v_1(p)= \int_{k_1}^{k_2} Q_1(p, r, v_1(r))dr+ \hslash_1(p)\) and \(v_2(p)= \int_{k_1}^{k_2} Q_2(p, r, v_2 (r))dr+ \hslash_2(p),\) where \(p\in[k_1, k_2], v_1, v_2, \hslash_1, \hslash_2\in V \), where \(V=C([k_1, k_2], \mathbb{R}^n)\) is the set of all real-valued continuous functions defined on \([k_1, k_2]\) and \(Q_1, Q_2:[k_1, k_2]\times[k_1, k_2]\times \mathbb{R}^n\longrightarrow \mathbb{R}^n\).