SOME STUDIES ON EULER-LAGRANGE QUARTIC FUNCTIONAL EQUATIONS IN <i>β</i>-NORMED SPACES

Jinyu Xia; Qi Liu; Yin Zhou; Zhiyong Rao; John Michael Rassias

doi:10.11948/20240405

2025 Volume 15 Issue 3

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Jinyu Xia, Qi Liu, Yin Zhou, Zhiyong Rao, John Michael Rassias. SOME STUDIES ON EULER-LAGRANGE QUARTIC FUNCTIONAL EQUATIONS IN β-NORMED SPACES[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1770-1785. doi: 10.11948/20240405

Citation:

Jinyu Xia, Qi Liu, Yin Zhou, Zhiyong Rao, John Michael Rassias. SOME STUDIES ON EULER-LAGRANGE QUARTIC FUNCTIONAL EQUATIONS IN β-NORMED SPACES[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1770-1785. doi: 10.11948/20240405

SOME STUDIES ON EULER-LAGRANGE QUARTIC FUNCTIONAL EQUATIONS IN β-NORMED SPACES

1.
School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
2.
International Joint Research Center of Simulation and Control for Population Ecology of Yangtze River in Anhui, Anqing Normal University, Anqing 246133, China
3.
Department of Mathematics and Informatics National and Kapodistrian University of Athens Attikis, 15342, Greece

Author Bio: Email: y23060036@stu.aqnu.edu.cn(J. Xia); Email: zhouyin0330@163.com(Y. Zhou); Email: 17855677860@163.com(Z. Rao); Email: jrassias@primedu.uoa.gr(J. M. Rassias)
Corresponding author: Email: liuq67@aqnu.edu.cn(Q. Liu)
Fund Project: The authors were supported by Anhui Province Higher Education Science Research Project (Natural Science), 2023AH050487

Abstract

Abstract

In this paper, we study two types of Euler-Lagrange functional equations that map $ \jmath $ from normed spaces to $ \beta $-normed spaces using quartic functional equations. We will investigate the inequality under various transformations and perturbations using both fixed point and direct methods, to establish the Hyers-Ulam stability of quartic Euler-Lagrange functional equations.
- Quartic functional equations /
- Hyers-Ulam stability /
- β-normed spaces /
- Euler-Lagrange functional equations
MSC: 39B52, 39B62, 47H10

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References

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