On a Weak Version of Hyers–Ulam Stability Theorem in Restricted Domains

Jaeyoung Chung () and Jeongwook Chang ()
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Jaeyoung Chung: Kunsan National University
Jeongwook Chang: Dankook University

A chapter in Handbook of Functional Equations, 2014, pp 113-133 from Springer

Abstract: Abstract In this chapter we consider a weak version of the Hyers–Ulam stability problem for the Pexider equation, Cauchy equation satisfied in restricted domains in a group when the target space of the functions is a 2-divisible commutative group. As the main result we find an approximate sequence for the unknown function satisfying the Pexider functional inequality, the limit of which is the approximate function in the Hyers–Ulam stability theorem.

Keywords: Hyers–Ulam stability; Functional equations; Restricted domains; Pexider equation; 2-divisible commutative group (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1286-5_6

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DOI: 10.1007/978-1-4939-1286-5_6

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