The authors consider a few problems concerning the stability for Lagrange’s and Flett’s mean value points. The first result reads as follows.
Let be a continuously twice differentiable mapping and let be a unique Lagrange’s mean value point of in (i.e., ). It is proved that for each there exists such that for each differentiable function satisfying , there exists a Lagrange’s mean value point of such that .
Other results are connected with approximate mean value points:
and with the stability of the equation: