In this paper we consider the equation $f(x)=0$ on the interval $D=[a,b]$, for a real - valued function $f$. We use the iterative method $x_{n+1}=\phi(x_n)$, $n=0,1,\dots,$ with a suitably chosen $\phi(x)$ and $x_0\in D$. We accept $x_{n+1}$ as a sufficiently accurate approximation of the exact solution a of the given equation, if we have $|x_{n+1}-x_n|<\varepsilon$, where $\varepsilon>0$ is the pre-assigned tolerance, and if the stopping inequality $|x_{n+1}-x_n|\geq|x_{n+1}-\alpha|$ is valid. For the special functions $phi$ we give sufficient conditions for the stopping inequality. As special cases we obtain both Newton's iterative method and the classical \emph{regula falsi} method. Moreover, we prove the stopping inequality for $n=0,1,\dots,$ for the class of iterative methods which are generated by inverse interpolation.