Point monotonicity of maps and its applications in numerical computation (Q702637)

Let \(I\subset \mathbb{R}\) be a nonempty set. A function \(f:I\rightarrow \mathbb{R}\) is said to be {monotone at} \(z\) if for every \(x\in I\) we have \[ (x-z)(f(x)-f(z))\geq 0 \] and {strictly monotone at }\(z\) if the previous inequality holds with `\(\geq\)' replaced by `\(>\)', for any \(x\in I\), \(x\neq z.\) The paper is concerned with the application of this concepts to the convergence of some numerical methods.