Some fixed point theorems for mappings of two variables (Q1775435)

Let \((X,d)\) be a complete metric space and \(T:X \times X \to X\) an operator. The author gives metric conditions on \(T\) which imply that: (i) \(T\) has at least one fixed point \(x\), i.e., \(x=T(x,x)\); (ii) for any \(x_0\in X\), the sequence \(x_n = T (x_n, x_{n-1})\) is well-defined for all \(n\geq 1\) and converges to a fixed point of \(T\).