Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)
In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2454 |
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| author | P. Agilan K. Julietraja Nabil Mlaiki Aiman Mukheimer |
| author_facet | P. Agilan K. Julietraja Nabil Mlaiki Aiman Mukheimer |
| author_sort | P. Agilan |
| collection | DOAJ |
| description | In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated. |
| first_indexed | 2024-03-09T17:56:47Z |
| format | Article |
| id | doaj.art-058659818fd24b8ca8cc0d51b58ea0c5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T17:56:47Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-058659818fd24b8ca8cc0d51b58ea0c52023-11-24T10:14:19ZengMDPI AGSymmetry2073-89942022-11-011411245410.3390/sym14112454Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)P. Agilan0K. Julietraja1Nabil Mlaiki2Aiman Mukheimer3Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai 600119, Tamil Nadu, IndiaDepartment of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai 600119, Tamil Nadu, IndiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaIn this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated.https://www.mdpi.com/2073-8994/14/11/2454Euler–Lagrange symmetry additive functional equationsgeneralised Hyers–Ulam–Rassiasstability intuitionistic fuzzy normed spacesfixed point technique |
| spellingShingle | P. Agilan K. Julietraja Nabil Mlaiki Aiman Mukheimer Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT) Symmetry Euler–Lagrange symmetry additive functional equations generalised Hyers–Ulam–Rassias stability intuitionistic fuzzy normed spaces fixed point technique |
| title | Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT) |
| title_full | Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT) |
| title_fullStr | Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT) |
| title_full_unstemmed | Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT) |
| title_short | Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT) |
| title_sort | intuitionistic fuzzy stability of an euler lagrange symmetry additive functional equation via direct and fixed point technique fpt |
| topic | Euler–Lagrange symmetry additive functional equations generalised Hyers–Ulam–Rassias stability intuitionistic fuzzy normed spaces fixed point technique |
| url | https://www.mdpi.com/2073-8994/14/11/2454 |
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