Abstract
The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers–Ulam–Rassias stability of the general quintic functional equation and the general sextic functional equation.
Highlights
Let X be a real normed space and Y be a real Banach space
In 1940, Ulam [1] raised the question about the stability of group of homomorphisms, and in the following year, Hyers [2] solved this question about the additive functional equation, which gave a partial answer to Ulam’s question
Many mathematicians have investigated the stability of different types of functional equations [9,10]
Summary
Let X be a real normed space and Y be a real Banach space. In 1940, Ulam [1] raised the question about the stability of group of homomorphisms, and in the following year, Hyers [2] solved this question about the additive functional equation, which gave a partial answer to Ulam’s question. Rassias [3] investigated the stability problem for approximately linear mappings controlled by the unbounded function θ (k x k p + kyk p ) as follow: Theorem 1. Let f : X → Y be a mapping from a real normed vector space X into a Banach space Y satisfying the inequality:. The functional equation is said to have Hyers–Ulam–Rassias stability when the stability can be proven under the control function θ (k x k p + kyk p ). A mapping f : X → Y is called a general quintic mapping if f satisfies the functional equation:.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
