Bibliographic Details
| Title: |
The Stability of Functional Equations with a New Direct Method |
| Authors: |
Dongwen Zhang, Qi Liu, John Michael Rassias, Yongjin Li |
| Source: |
Mathematics, Vol 10, Iss 7, p 1188 (2022) |
| Publisher Information: |
MDPI AG, 2022. |
| Publication Year: |
2022 |
| Collection: |
LCC:Mathematics |
| Subject Terms: |
Hyers–Ulam stability, functional equations, approximation, the direct method, the convergence series, Mathematics, QA1-939 |
| More Details: |
We investigate the Hyers–Ulam stability of an equation involving a single variable of the form ∥f(x)−αf(kn(x))−βf(kn+1(x))∥⩽u(x) where f is an unknown operator from a nonempty set X into a Banach space Y, and it preserves the addition operation, besides other certain conditions. The theory is employed and stability theorems are proven for various functional equations involving several variables. By comparing this method with the available techniques, it was noticed that this method does not require any restriction on the parity, on the domain, and on the range of the function. Our findings suggest that it is very much easy and more appropriate to apply the proposed method while investigating the stability of functional equations, in particular for several variables. |
| Document Type: |
article |
| File Description: |
electronic resource |
| Language: |
English |
| ISSN: |
2227-7390 |
| Relation: |
https://www.mdpi.com/2227-7390/10/7/1188; https://doaj.org/toc/2227-7390 |
| DOI: |
10.3390/math10071188 |
| Access URL: |
https://doaj.org/article/f94cad527f8a47489311a33e81d1bd7b |
| Accession Number: |
edsdoj.f94cad527f8a47489311a33e81d1bd7b |
| Database: |
Directory of Open Access Journals |
