Abstract
We aim to introduce the quadratic-additive functional equation (shortly, QA-functional equation) and find its general solution. Then, we study the stability of the kind of Hyers-Ulam result with a view of the aforementioned functional equation by utilizing the technique based on a fixed point in the framework of β-Banach modules. We here discuss our results for odd and even mappings as well as discuss the stability of mixed cases.
Highlights
In 1940, Ulam [1] inquired about the stability of groups of homomorphisms: “What is an additive mapping in close range to an additive mapping of a group and a metric group?” In the year, Hyers [2] responded affirmatively to the above query for more groups, assuming that Banach spaces are the groups
Cădariu and Radu used the fixed point approach to prove the stability of the Cauchy functional equation in 2002
We introduce a new kind of generalized quadratic-additive functional equation is
Summary
In 1940, Ulam [1] inquired about the stability of groups of homomorphisms: “What is an additive mapping in close range to an additive mapping of a group and a metric group?” In the year, Hyers [2] responded affirmatively to the above query for more groups, assuming that Banach spaces are the groups. Gavruta [4] has demonstrated the stability of Hyers-Ulam-Rassias with its enhanced control function. This stability finding is the stability of Hyers-Ulam-Rassias functional equations. Baker [5] utilized the Banach fixed point theorem to provide a Hyers-Ulam stability result. Cădariu and Radu used the fixed point approach to prove the stability of the Cauchy functional equation in 2002. They planned to use the fixed-point alternative theorem [6]
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