Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean Spaces
In this paper, we investigated the asymptotic stability behaviour of the Pexider–Cauchy functional equation in non-Archimedean spaces. We also showed that, under some conditions, if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-09-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/18/2197 |
| _version_ | 1829092024262852608 |
|---|---|
| author | Hamid Gharib Mohammad B. Moghimi Abbas Najati Jae-Hyeong Bae |
| author_facet | Hamid Gharib Mohammad B. Moghimi Abbas Najati Jae-Hyeong Bae |
| author_sort | Hamid Gharib |
| collection | DOAJ |
| description | In this paper, we investigated the asymptotic stability behaviour of the Pexider–Cauchy functional equation in non-Archimedean spaces. We also showed that, under some conditions, if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∥</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>)</mo><mo>−</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><mi>h</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>∥</mo><mo>⩽</mo><mi>ε</mi></mrow></semantics></math></inline-formula>, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></semantics></math></inline-formula> and <i>h</i> can be approximated by additive mapping in non-Archimedean normed spaces. Finally, we deal with a functional inequality and its asymptotic behaviour. |
| first_indexed | 2024-03-10T07:28:34Z |
| format | Article |
| id | doaj.art-f95a972f449544e88d9b305df6d6be84 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T07:28:34Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f95a972f449544e88d9b305df6d6be842023-11-22T14:04:44ZengMDPI AGMathematics2227-73902021-09-01918219710.3390/math9182197Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean SpacesHamid Gharib0Mohammad B. Moghimi1Abbas Najati2Jae-Hyeong Bae3Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, IranDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, IranDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, IranHumanitas College, Kyung Hee University, Yongin 17104, KoreaIn this paper, we investigated the asymptotic stability behaviour of the Pexider–Cauchy functional equation in non-Archimedean spaces. We also showed that, under some conditions, if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∥</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>)</mo><mo>−</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><mi>h</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>∥</mo><mo>⩽</mo><mi>ε</mi></mrow></semantics></math></inline-formula>, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></semantics></math></inline-formula> and <i>h</i> can be approximated by additive mapping in non-Archimedean normed spaces. Finally, we deal with a functional inequality and its asymptotic behaviour.https://www.mdpi.com/2227-7390/9/18/2197non-Archimedean spacePexider–Cauchy equationasymptotic stability |
| spellingShingle | Hamid Gharib Mohammad B. Moghimi Abbas Najati Jae-Hyeong Bae Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean Spaces Mathematics non-Archimedean space Pexider–Cauchy equation asymptotic stability |
| title | Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean Spaces |
| title_full | Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean Spaces |
| title_fullStr | Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean Spaces |
| title_full_unstemmed | Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean Spaces |
| title_short | Asymptotic Stability of the Pexider–Cauchy Functional Equation in Non-Archimedean Spaces |
| title_sort | asymptotic stability of the pexider cauchy functional equation in non archimedean spaces |
| topic | non-Archimedean space Pexider–Cauchy equation asymptotic stability |
| url | https://www.mdpi.com/2227-7390/9/18/2197 |
| work_keys_str_mv | AT hamidgharib asymptoticstabilityofthepexidercauchyfunctionalequationinnonarchimedeanspaces AT mohammadbmoghimi asymptoticstabilityofthepexidercauchyfunctionalequationinnonarchimedeanspaces AT abbasnajati asymptoticstabilityofthepexidercauchyfunctionalequationinnonarchimedeanspaces AT jaehyeongbae asymptoticstabilityofthepexidercauchyfunctionalequationinnonarchimedeanspaces |