In the next year, Donald H. Hyers[1] gave a partial affirmative answer to the question of Ulam in the context of Banach spaces in the case of additive mappings, that was the first significant breakthrough and a step toward more solutions in this area.
Since then, a large number of papers have been published in connection with various generalizations of Ulam's problem and Hyers's theorem.
This result of Rassias attracted several mathematicians worldwide who began to be stimulated to investigate the stability problems of functional equations.
For an extensive presentation of the stability of functional equations in the context of Ulam's problem, the interested reader is referred to the books by S.-M. Jung,[5] S. Czerwik,[6] Y.J.
[10][11][12][13] In 1950, T. Aoki[14] considered an unbounded Cauchy difference which was generalised later by Rassias to the linear case.