Functional analysis is an important branch of mathematics widely used to study the stability of different functional equations. This includes the stability of various quadratic functional equations, which typically involve a specific number of variables to reach results more easily in this field. One of the methods used to study the stability of functional equations is the direct method, which is known for its simplicity in proving the stability of this type of functional equation. In this research paper, we have successfully proven the Hyers-Ulam-Rassias stability of the quadratic functional equation in 2-Banach spaces. Specifically, we have shown that the equation: f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(x+z) holds true within this context. Our approach involved using either the usual or the direct method to establish this stability. Furthermore, we have also demonstrated the generalized Hyers-Ulam stability of the quadratic functional equation in 2-Banach spaces using the usual process by considering various conditions. This has led to many exciting results and revealed many related applications.
| Published in | American Journal of Applied Mathematics (Volume 12, Issue 6) |
| DOI | 10.11648/j.ajam.20241206.11 |
| Page(s) | 200-213 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Hyers-Ulam Stability, 2-Banach Spaces, Quadratic Mapping, Functional Equation, Usual Method
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APA Style
Zenada, F. S. A., Elmaged, E. A. A. (2024). Stability of Quadratic Mappings in 2-Banach Spaces and Related Topics. American Journal of Applied Mathematics, 12(6), 200-213. https://doi.org/10.11648/j.ajam.20241206.11
ACS Style
Zenada, F. S. A.; Elmaged, E. A. A. Stability of Quadratic Mappings in 2-Banach Spaces and Related Topics. Am. J. Appl. Math. 2024, 12(6), 200-213. doi: 10.11648/j.ajam.20241206.11
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Download@article{10.11648/j.ajam.20241206.11,
author = {Fadi S. Abu Zenada and Eltayeb A. Abed Elmaged},
title = {Stability of Quadratic Mappings in 2-Banach Spaces and Related Topics},
journal = {American Journal of Applied Mathematics},
volume = {12},
number = {6},
pages = {200-213},
doi = {10.11648/j.ajam.20241206.11},
url = {https://doi.org/10.11648/j.ajam.20241206.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20241206.11},
abstract = {Functional analysis is an important branch of mathematics widely used to study the stability of different functional equations. This includes the stability of various quadratic functional equations, which typically involve a specific number of variables to reach results more easily in this field. One of the methods used to study the stability of functional equations is the direct method, which is known for its simplicity in proving the stability of this type of functional equation. In this research paper, we have successfully proven the Hyers-Ulam-Rassias stability of the quadratic functional equation in 2-Banach spaces. Specifically, we have shown that the equation: f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(x+z) holds true within this context. Our approach involved using either the usual or the direct method to establish this stability. Furthermore, we have also demonstrated the generalized Hyers-Ulam stability of the quadratic functional equation in 2-Banach spaces using the usual process by considering various conditions. This has led to many exciting results and revealed many related applications.},
year = {2024}
}
TY - JOUR T1 - Stability of Quadratic Mappings in 2-Banach Spaces and Related Topics AU - Fadi S. Abu Zenada AU - Eltayeb A. Abed Elmaged Y1 - 2024/11/11 PY - 2024 N1 - https://doi.org/10.11648/j.ajam.20241206.11 DO - 10.11648/j.ajam.20241206.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 200 EP - 213 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20241206.11 AB - Functional analysis is an important branch of mathematics widely used to study the stability of different functional equations. This includes the stability of various quadratic functional equations, which typically involve a specific number of variables to reach results more easily in this field. One of the methods used to study the stability of functional equations is the direct method, which is known for its simplicity in proving the stability of this type of functional equation. In this research paper, we have successfully proven the Hyers-Ulam-Rassias stability of the quadratic functional equation in 2-Banach spaces. Specifically, we have shown that the equation: f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(x+z) holds true within this context. Our approach involved using either the usual or the direct method to establish this stability. Furthermore, we have also demonstrated the generalized Hyers-Ulam stability of the quadratic functional equation in 2-Banach spaces using the usual process by considering various conditions. This has led to many exciting results and revealed many related applications. VL - 12 IS - 6 ER -
Mathematics Department, Faculty of Science, University of Holly Quran and Taseel of Science, Khartoum, Sudan
Mathematics Department, Faculty of Science, University of Holly Quran and Taseel of Science, Khartoum, Sudan
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