Fuzzy Stability Results of Generalized Quartic Functional Equations
In the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques. We provide some applications in which the stability of this quartic functional equation can be controlle...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/2/120 |
| _version_ | 1797415144348712960 |
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| author | Sang Og Kim Kandhasamy Tamilvanan |
| author_facet | Sang Og Kim Kandhasamy Tamilvanan |
| author_sort | Sang Og Kim |
| collection | DOAJ |
| description | In the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques. We provide some applications in which the stability of this quartic functional equation can be controlled by sums and products of powers of norms. In particular, we show that if the control function is the fuzzy norm of the product of powers of norms, the quartic functional equation is hyperstable. |
| first_indexed | 2024-03-09T05:44:37Z |
| format | Article |
| id | doaj.art-de82d3b3d26346169c07bd213c0274cd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:44:37Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-de82d3b3d26346169c07bd213c0274cd2023-12-03T12:22:50ZengMDPI AGMathematics2227-73902021-01-019212010.3390/math9020120Fuzzy Stability Results of Generalized Quartic Functional EquationsSang Og Kim0Kandhasamy Tamilvanan1School of Data Science, Hallym University, Chuncheon 24252, KoreaDepartment of Mathematics, Government Arts College for Men, Krishnagiri 635 001, IndiaIn the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques. We provide some applications in which the stability of this quartic functional equation can be controlled by sums and products of powers of norms. In particular, we show that if the control function is the fuzzy norm of the product of powers of norms, the quartic functional equation is hyperstable.https://www.mdpi.com/2227-7390/9/2/120quartic functional equationHyers–Ulam stabilityfixed pointfuzzy normed space |
| spellingShingle | Sang Og Kim Kandhasamy Tamilvanan Fuzzy Stability Results of Generalized Quartic Functional Equations Mathematics quartic functional equation Hyers–Ulam stability fixed point fuzzy normed space |
| title | Fuzzy Stability Results of Generalized Quartic Functional Equations |
| title_full | Fuzzy Stability Results of Generalized Quartic Functional Equations |
| title_fullStr | Fuzzy Stability Results of Generalized Quartic Functional Equations |
| title_full_unstemmed | Fuzzy Stability Results of Generalized Quartic Functional Equations |
| title_short | Fuzzy Stability Results of Generalized Quartic Functional Equations |
| title_sort | fuzzy stability results of generalized quartic functional equations |
| topic | quartic functional equation Hyers–Ulam stability fixed point fuzzy normed space |
| url | https://www.mdpi.com/2227-7390/9/2/120 |
| work_keys_str_mv | AT sangogkim fuzzystabilityresultsofgeneralizedquarticfunctionalequations AT kandhasamytamilvanan fuzzystabilityresultsofgeneralizedquarticfunctionalequations |