Abstract
We prove the generalized Hyers–Ulam stability of a mean value type functional equation f ( x ) − g ( y ) = ( x − y ) h ( x + y ) by applying a method originated from fixed point theory.
Highlights
Ulam [1] proposed the stability problem of functional equations: “Suppose G1 is a group and G2 is a metric group with the metric d(·, ·)
Hyers [2] proved that every solution to the inequality k f ( x + y) − f ( x ) − f (y)k ≤ ε can be approximated by an additive function
The Cauchy additive equation is said to satisfy the Hyers–Ulam stability. This terminology is applied to the case of other functional equations
Summary
Ulam [1] proposed the stability problem of functional equations:“Suppose G1 is a group and G2 is a metric group with the metric d(·, ·). We investigate the generalized Hyers–Ulam stability of the mean value type functional Equation (2) by using a method originated from fixed point theory in the sense of Cădariu and Radu (see [14,15,16]).
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