ON THE STABILITY OF THE CAUCHY FUNCTIONAL EQUATION: A FIXED POINT APPROACH

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A Fixed Point Approach to the Stability of a Volterra Integral Equation (2007, methodology): “Hyers-Ulam-Rassias stability Recently, Cădariu and Radu [12] applied the fixed point method to the investigation of the Cauchy additive functional equation.”
A fixed point approach to the stability of the cubic functional equation (2006, methodology): “Radu [3] applied the fixed point method to the investigation of the Cauchy additive functional equation (ref.”
Approximately generalized additive functions in several variables (2010, methodology): “Let Ω be the set of all functions g : X → Y and introduce a generalized metric on Ω as follows: d(g, h) = dψ(g, h) = inf{K ∈ (0,∞) : ‖g(x)− h(x)‖ ≤ Kψ(x), x ∈ X} It is easy to show that (Ω, d) is a generalized complete metric space [11].”
A fixed point approach to the stability of isometries (2007, methodology): “Radu [8] applied the fixed point method to the investigation of the Cauchy additive functional equation (refs.”
Hyers-Ulam-Rassias Stability for a First Order Functional Differential Equation (2015, methodology): “Since then, the stability problems of various functional equations have been investigated by many authors (see [1-17]).”