Hyers-Ulam-Gavruta stability of a Jensen's type quadratic-quadratic mapping in 2-Banach spaces
Authors
S. Murugesan
- Department of Mathematics, Sree Abiraami Arts \(\&\) Science College for Women, Gudiyattam, Vellore Dt. - 635 803, Tamil Nadu, India.
P. S. Arumugam
- Department of Mathematics, Rajalakshmi Engineering College (Autonomous), Thandalam, Chennai - 602105, Tamil Nadu, India.
G. Gandhi
- Department of Mathematics, R.M.D Engineering College, Kavaraipettai, Thiruvallur Dt. - 601 206, Tamil Nadu, India.
V. Mani
- Department of Mathematics, School of Advanced Science, Vellore Institute of Technology, Vellore - 632 014, Tamil Nadu, India.
S. Srinivasan
- Department of Mathematics, Panimalar Engineering College, Chennai, Tamil Nadu, India.
Abstract
In this paper, our main objective is to study the Hyers-Ulam-Gavruta stability of a Jensen's type quadratic-quadratic mapping in 2-Banach Spaces, that is, we prove the Hyers-Ulam-Gavruta stability of the Jensen's type functional equation
\[ g \left( \dfrac{x+y}{2} + z \right) + g \left( \dfrac{x+y}{2} - z \right) + g \left( \dfrac{x-y}{2} + z \right) + g \left( \dfrac{x-y}{2} - z \right) = g(x) + g(y) + 4 g(z) ,\]
in 2-Banach spaces by Hyers direct method.
Share and Cite
ISRP Style
S. Murugesan, P. S. Arumugam, G. Gandhi, V. Mani, S. Srinivasan, Hyers-Ulam-Gavruta stability of a Jensen's type quadratic-quadratic mapping in 2-Banach spaces, Journal of Mathematics and Computer Science, 32 (2024), no. 4, 295--317
AMA Style
Murugesan S., Arumugam P. S., Gandhi G., Mani V., Srinivasan S., Hyers-Ulam-Gavruta stability of a Jensen's type quadratic-quadratic mapping in 2-Banach spaces. J Math Comput SCI-JM. (2024); 32(4):295--317
Chicago/Turabian Style
Murugesan, S., Arumugam, P. S., Gandhi, G., Mani, V., Srinivasan, S.. "Hyers-Ulam-Gavruta stability of a Jensen's type quadratic-quadratic mapping in 2-Banach spaces." Journal of Mathematics and Computer Science, 32, no. 4 (2024): 295--317
Keywords
- Hyers-Ulam-Gavruta stability
- Jensen's type mapping
- quadratic function
- invex set
- direct method
MSC
- 39B82
- 39B52
- 46B99
- 39B72
- 39B22
- 34K20
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