Development of the Additive-Quadratic η-Function Inequality with 3k-Variables Based on a General Quadratic Function Variables on a Complex Banach Spaces
In this article, I study the establishment of the quadratic-additive η-function inequality with 3k-variables on the homogeneous complex Banach space and prove the quadratic-additive η-function equation related to the additive and quadratic η-functional inequalities in (α1,α2)-homogeneous Banach complex space.
Cite this paper
An, L. V. (2023). Development of the Additive-Quadratic η-Function Inequality with 3k-Variables Based on a General Quadratic Function Variables on a Complex Banach Spaces. Open Access Library Journal, 10, e777. doi: http://dx.doi.org/10.4236/oalib.1110777.
Hyers, D.H. (1941) On the Stability of the Linear Functional Equation. Proceedings of the National Academy of Sciences of the United States of America, 27, 222-224.
https://doi.org/10.1073/pnas.27.4.222
Aoki, T. (1950) On the Stability of the Linear Transformation in Banach Spaces. Journal of the Mathematical Society of Japan, 2, 64-66.
https://doi.org/10.2969/jmsj/00210064
Rassias, Th.M. (1978) On the Stability of the Linear Mapping in Banach Spaces. Proceedings of the AMS, 72, 297-300.
https://doi.org/10.1090/S0002-9939-1978-0507327-1
Găvruta, P. (1994) A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings. Journal of Mathematical Analysis and Applications, 184, 431-436. https://doi.org/10.1006/jmaa.1994.1211
Fechner, W. (2006) Stability of a Functional Inequalities Associated with the Jordan-von Neumann Functional Equation. Aequationes Mathematicae, 71, 149-161.
https://doi.org/10.1007/s00010-005-2775-9
Lee, J.R., Park, C. and Shin, D.Y. (2014) Additive and Quadratic Functional in Equalities in Non-Archimedean Normed Spaces. International Journal of Mathematical Analysis, 8, 1233-1247. https://doi.org/10.12988/ijma.2014.44113
Lee, H., Cha, J.Y., Cho, M.W. and Kwon, M. (2016) Additive ρ-Functional Inequalities in β-Homogeneous F-Spaces. Journal of the Korean Society of Mathematical Education Series B-Pure and Applied Mathematics, 23, 319-328.
https://doi.org/10.7468/jksmeb.2016.23.3.319
Park, C., Cho, Y. and Han, M. (2007) Functional Inequalities Associated with Jordan-von Newman-Type Additive Functional Equations. Journal of Inequalities and Applications, 2007, Article ID: 041820. https://doi.org/10.1155/2007/41820
Prager, W. and Schwaiger, J. (2013) A System of Two in Homogeneous Linear Functional Equations. Acta Mathematica Hungarica, 140, 377-406.
https://doi.org/10.1007/s10474-013-0315-y
Park, C. (2014) Additive β-Functional Inequalities. Journal of Nonlinear Sciences and Applications, 7, 296-310. https://doi.org/10.22436/jnsa.007.05.02
Van An, L. (2020) Generalized Hyers-Ulam Type Stability of the Type Functional Equation with 2k-Variable in Non-Archimedean Space. Asia Mathematika, 5, 69- 83.
Van An, L. (2020) Generalized Hyers-Ulam Type Stability of the Additive Functional Equation Inequalities with 2n-Variables on an Approximate Group and Ring Homomorphism. Asia Mathematika, 4, 161-175.
Van An, L. (2021) Generalized Hyers-Ulam-Rassias Type Stability of the with 2k-Variable Quadratic Functional Inequalities in Non-Archimedean Banach Spaces and Banach Spaces. Asia Mathematika, 5, 69-83.
https://doi.org/10.14445/22315373/IJMTT-V67I9P521
Van An, L. (2021) Generalized Hyers-Ulam Type Stability of the 2k-Variables Quadratic β-Functional Inequalities and Function in γ-Homogeneous Normed Space. International Journal of Mathematics and Its Applications, 9, 81-93.
Van An, L. (2023) Generalized Stability of Functional Inequalities with 3k-Variables Associated for Jordan-von Neumann-Type Additive Functional Equation. Open Access Library Journal, 10, e9681.
Van An, L. (2020) Generalized Hyers-Ulam Type Stability of the 2k-Variable Additive β-Functional Inequalities and Equations in Complex Banach Space. International Journal of Mathematics Trends and Technology, 66, 134-147.
https://doi.org/10.14445/22315373/IJMTT-V66I7P518
Van An, L. (2022) Generalized Stability Additive λ-Functional Inequalities with 3k-Variable in α-Homogeneous F-Spaces. International Journal of Analysis and Applications, 20, 43. https://doi.org/10.28924/2291-8639-20-2022-43
Skof, F. (1983) Proprieta’ locali e approssimazione di operatori. Rendiconti del Seminario Matematico e Fisico di Milano, 53, 113-129.
https://doi.org/10.1007/BF02924890
Bahyrycz, A. and Piszczek, M. (2014) Hyers Stability of the Jensen Function Equation. Acta Mathematica Hungarica, 142, 353-365.
https://doi.org/10.1007/s10474-013-0347-3
Balcerowski, M. (2013) On the Functional Equations Related to a Problem of Z Boros and Z. Dróczy. Acta Mathematica Hungarica, 138, 329-340.
https://doi.org/10.1007/s10474-012-0278-4
