Hyers-Ulam Stability of Two-Dimensional Flett's Mean Value Points

Abstract

If a differentiable function f : [a,b]-> R and a point eta is an element of[a,b] satisfy f(eta)-f(a)=f '(eta)(eta-a), then the point eta is called a Flett's mean value point of f in [a,b]. The concept of Flett's mean value points can be generalized to the 2-dimensional Flett's mean value points as follows: For the different points (r) over cap and (s) over cap of R x R, let L be the line segment joining (r) over cap and (s) over cap. If a partially differentiable function f : RxR -> R and an intermediate point (omega) over cap is an element of L satisfy f((omega) over cap)-f((r) over cap)=<(omega)over cap>-(r) over cap ,f '(<(omega)over cap)>, then the point <(omega)over cap> is called a 2-dimensional Flett's mean value point of f in L. In this paper, we will prove the Hyers-Ulam stability of 2-dimensional Flett's mean value points.