Generalized Hyers-Ulam-Rassisa Stability of an Additive (β1,β2)-Functional Inequalities with n-Variables in Complex Banach Space

doi:10.4236/oalib.1109183

OALib Journal期刊
ISSN: 2333-9721
费用：99美元

查看量	下载量

Open Access Library Journal 9 2022

查看所有领域

Generalized Hyers-Ulam-Rassisa Stability of an Additive (β₁,β₂)-Functional Inequalities with n-Variables in Complex Banach Space

DOI: 10.4236/oalib.1109183, PP. 1-14

Ly Van An

Subject Areas: Mathematics

Keywords: Additive (β1,β2)-Functional Inequality, Fixed Point Method, Direct Method, Banach Space, Hyers-Ulam Stability

Full-Text Cite this paper Add to My Lib

Abstract

In this paper, we study to solve the additive (β₁,β₂)-functional inequality with n-variables and their Hyers-Ulam stability. First are investigated in complex Banach spaces with a fixed point method and last are investigated in complex Banach spaces with a direct method. These are the main results of this paper.

Cite this paper

An, L. V. (2022). Generalized Hyers-Ulam-Rassisa Stability of an Additive (β1,β2)-Functional Inequalities with n-Variables in Complex Banach Space. Open Access Library Journal, 9, e9183. doi: http://dx.doi.org/10.4236/oalib.1109183.

References

[1]	Ulam, S.M. (1960) A Collection of Mathematical Problems. Vol. 8, Interscience Publishers, New York.
[2]	Hyers, D.H. (1941) On the Stability of the 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
[3]	Aoki, T. (1950) On the Stability of the Linear Transformation in Banach Space. Journal of the Mathematical Society of Japan, 2, 64-66. https://doi.org/10.2969/jmsj/00210064
[4]	Rassias, T.M. (1978) On the Stability of the Linear Mapping in Banach Space. Proceedings of the American Mathematical Society, 27, 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
[5]	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
[6]	Skof, F. (1983) Propriet locali e approssimazione di operatori. Rendiconti del Seminario Matematico e Fisico di Milano, 53, 113-129. https://doi.org/10.1007/BF02924890
[7]	Park, C. (2015) Additive ρ-Functional Inequalities and Equations. Journal of Mathematical Inequalities, 9, 17-26. https://doi.org/10.7153/jmi-09-02
[8]	Park, C. (2015) Additive ρ-Functional Inequalities in Non-Archimedean Normed Spaces. Journal of Mathematical Inequalities, 9, 397-407. https://doi.org/10.7153/jmi-09-33
[9]	Fechner, W. (2010) On Some Functional Inequalities Related to the Logarithmic mean. Acta Mathematica Hungarica, 128, 31-45. https://doi.org/10.1007/s10474-010-9153-3
[10]	Fechner, W. (2006) Stability of a Functional Inequlities Associated with the Jordan-Von Neumann Functional Equation. Aequationes Mathematicae, 71, 149-161. https://doi.org/10.1007/s00010-005-2775-9
[11]	Cadariu, L. and Radu, V. (2003) Fixed Points and the Stability of Jensen’s Functional Equation. Journal of Inequalities in Pure and Applied Mathematics, 4, Article No. 4.
[12]	Diaz, J. and Margolis, B. (1968) A Fixed Point Theorem of the Alternative for Contractions on a Generalized Complete Metric Space. Bulletin of the American Mathematical Society, 74, 305-309. https://doi.org/10.1090/S0002-9904-1968-11933-0
[13]	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
[14]	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
[15]	Gilányi, A. (2002) On a Problem by K. Nikodem. Mathematical Inequalities & Applications, 5, 707-710. https://doi.org/10.7153/mia-05-71
[16]	Gilányi, A. (2002) Eine zur parallelogrammleichung äquivalente ungleichung. Aequationes Mathematicae, 62, 303-309. https://doi.org/10.7153/mia-05-71
[17]	Qarawani, M.N. (2012) Hyers-Ulam Stability of a Generalized Second-Order Nonlinear Differential Equation. Applied Mathematics, 3, 1857-1861. https://doi.org/10.4236/am.2012.312252 http://www.scirp.org/journal/am
[18]	Park, C., Cho, Y. and Han, M. (2007) Functional Inequalities Associated with Jordanvon Newman-Type Additive Functional Equations. Journal of Inequalities and Applications, 2007, Article No. 41820, 13 p. https://doi.org/10.1155/2007/41820
[19]	Rätz, J. (2003) On Inequalities Assosciated with the Jordan-Von Neumann Functional Equation. Aequationes Mathematicae, 66, 191-200. https://doi.org/10.1007/s00010-003-2684-8
[20]	Park, C. (2014) Additive β-Functional Inequalities. Journal of Nonlinear Science and Applications, 7, 296-310. https://doi.org/10.22436/jnsa.007.05.02
[21]	Van An, L. (2019) Hyers-Ulam Stability of Functional Inequalities with Three Variable in Banach Spaces and Non-Archemdean Banach Spaces. International Journal of Mathematical Analysis, 13, 519-530. https://doi.org/10.12988/ijma.2019.9954
[22]	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
[23]	Yun, S.S. and Shin, Dong, Y. (2017) Stability of an Additive (p₁,p₂)-Functional Inequality in Banach Spaces. The Pure and Applied Mathematics, 24, 21-31. https://doi.org/10.7468/jksmeb.2017.24.1.21
[24]	Van An, L.Y. (2020) Hyers-Ulam stability of β-Functional Inequalities with Three Variable in Non-Archemdean Banach Spaces and Complex Banach. International Journal of Mathematical Analysis, 14, 219-239. https://doi.org/10.12988/ijma.2020.91169 http://www.m-hikari.com/
[25]	Mihet, D. and Radu, V. (2008) On the Stability of the Additive Cauchy Functional Equation in Random Normed Spaces. Journal of Mathematical Analysis and Applications, 343, 567-572. https://doi.org/10.1016/j.jmaa.2008.01.100

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133