A fixed point theorem for a system of Pachpatte operator equations (Q2662881)

The authors study the solvability of the fixed point equation \(Tx= x\), subject to the constraints \(\alpha_1(x)=\cdots = \alpha_r(x)= 0\), where \(T\) and \(\alpha_i\) \((i=1, 2,\dots, r)\) are operators in a Banach space with cone. B. Samet [\textit{A. H. Ansari} et al., J. Fixed Point Theory Appl. 19, No. 2, 1145--1163 (2017; Zbl 1454.47060)] has proved the existence of a solution building on a fixed point theorem by \textit{L. B. Čirić} [Publ. Inst. Math., Nouv. Sér. 17(31), 52--58 (1974; Zbl 0309.54035)]. In this paper, the authors prove existence by means of another fixed point theorem by \textit{B. G. Pachpatte} [Indian J. Pure Appl. Math. 10, 1039--1043 (1979; Zbl 0412.54053)].