STABILITY OF GENERAL QUADRATIC EULER–LAGRANGE FUNCTIONAL EQUATIONS IN MODULAR SPACES: A FIXED POINT APPROACH
In this paper, we establish a result on the Hyers–Ulam–Rassias stability of the Euler–Lagrange functional equation. The work presented here is in the framework of modular spaces. We obtain our results by applying a fixed point theorem. Moreover, we do not use the \(\Delta_\alpha\)-condition of modu...
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2025-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/853 |
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| author | Parbati Saha Pratap Mondal Binayak S. Choudhuary |
| author_facet | Parbati Saha Pratap Mondal Binayak S. Choudhuary |
| author_sort | Parbati Saha |
| collection | DOAJ |
| description | In this paper, we establish a result on the Hyers–Ulam–Rassias stability of the Euler–Lagrange functional equation. The work presented here is in the framework of modular spaces. We obtain our results by applying a fixed point theorem. Moreover, we do not use the \(\Delta_\alpha\)-condition of modular spaces in the proofs of our theorems, which introduces additional complications in establishing stability. We also provide some corollaries and an illustrative example. Apart from its main objective of obtaining a stability result, the present paper also demonstrates how fixed point methods are applicable in modular spaces. |
| format | Article |
| id | doaj-art-0bb2c0f0d0a749ca8a26d28080d5860e |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-0bb2c0f0d0a749ca8a26d28080d5860e2025-08-20T02:47:59ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522025-07-0111110.15826/umj.2025.1.008229STABILITY OF GENERAL QUADRATIC EULER–LAGRANGE FUNCTIONAL EQUATIONS IN MODULAR SPACES: A FIXED POINT APPROACHParbati Saha0Pratap Mondal1Binayak S. Choudhuary2Indian Institute of Engineering Science and Technology, Shibpur, Howrah – 711103, West BengalBijoy Krishna Girls’ College, Howrah, Howrah – 711101, West BengalIndian Institute of Engineering Science and Technology, Shibpur, Howrah – 711103, West BengalIn this paper, we establish a result on the Hyers–Ulam–Rassias stability of the Euler–Lagrange functional equation. The work presented here is in the framework of modular spaces. We obtain our results by applying a fixed point theorem. Moreover, we do not use the \(\Delta_\alpha\)-condition of modular spaces in the proofs of our theorems, which introduces additional complications in establishing stability. We also provide some corollaries and an illustrative example. Apart from its main objective of obtaining a stability result, the present paper also demonstrates how fixed point methods are applicable in modular spaces.https://umjuran.ru/index.php/umj/article/view/853hyers–ulam–rassias stability, euler–lagrange functional equation, modular spaces, convexity, fixed point method |
| spellingShingle | Parbati Saha Pratap Mondal Binayak S. Choudhuary STABILITY OF GENERAL QUADRATIC EULER–LAGRANGE FUNCTIONAL EQUATIONS IN MODULAR SPACES: A FIXED POINT APPROACH Ural Mathematical Journal hyers–ulam–rassias stability, euler–lagrange functional equation, modular spaces, convexity, fixed point method |
| title | STABILITY OF GENERAL QUADRATIC EULER–LAGRANGE FUNCTIONAL EQUATIONS IN MODULAR SPACES: A FIXED POINT APPROACH |
| title_full | STABILITY OF GENERAL QUADRATIC EULER–LAGRANGE FUNCTIONAL EQUATIONS IN MODULAR SPACES: A FIXED POINT APPROACH |
| title_fullStr | STABILITY OF GENERAL QUADRATIC EULER–LAGRANGE FUNCTIONAL EQUATIONS IN MODULAR SPACES: A FIXED POINT APPROACH |
| title_full_unstemmed | STABILITY OF GENERAL QUADRATIC EULER–LAGRANGE FUNCTIONAL EQUATIONS IN MODULAR SPACES: A FIXED POINT APPROACH |
| title_short | STABILITY OF GENERAL QUADRATIC EULER–LAGRANGE FUNCTIONAL EQUATIONS IN MODULAR SPACES: A FIXED POINT APPROACH |
| title_sort | stability of general quadratic euler lagrange functional equations in modular spaces a fixed point approach |
| topic | hyers–ulam–rassias stability, euler–lagrange functional equation, modular spaces, convexity, fixed point method |
| url | https://umjuran.ru/index.php/umj/article/view/853 |
| work_keys_str_mv | AT parbatisaha stabilityofgeneralquadraticeulerlagrangefunctionalequationsinmodularspacesafixedpointapproach AT pratapmondal stabilityofgeneralquadraticeulerlagrangefunctionalequationsinmodularspacesafixedpointapproach AT binayakschoudhuary stabilityofgeneralquadraticeulerlagrangefunctionalequationsinmodularspacesafixedpointapproach |