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

If a differentiable function f : [ a , b ] → R and a point η ∈ [ a , b ] satisfy f ( η ) - f ( a ) = f ′ ( η ) ( η - a ) , then the point η 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 ^ and s ^ of R × R , let L be the line segment joining r ^ and s ^ . If a partially differentiable function f : R × R → R and an intermediate point ω ^ ∈ L satisfy f ( ω ^ ) - f ( r ^ ) = ω ^ - r ^ , f ′ ( ω ^ ) , then the point ω ^ 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.