全部 标题 作者
关键词 摘要

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

查看量下载量

Generalized Hyers-Ulam-Rassias Type Stability Additive α-Functional Inequalities with 3k-Variable in Complex Banach Spaces

DOI: 10.4236/oalib.1109373, PP. 1-13

Subject Areas: Mathematics

Keywords: Additive β-Functional Equation, Additive β-Functional Inequality, Complex Banach Space, Hyers-Ulam-Rassisa Stability

Full-Text   Cite this paper   Add to My Lib

Abstract

In this paper we study to solve two-additive α-functional inequality with 3k-variables and their Hyers-Ulam-Rassias type stability. It is investigated in complex Banach spaces. These are the main results of this paper.

Cite this paper

An, L. V. (2022). Generalized Hyers-Ulam-Rassias Type Stability Additive α-Functional Inequalities with 3k-Variable in Complex Banach Spaces. Open Access Library Journal, 9, e9373. doi: http://dx.doi.org/10.4236/oalib.1109373.

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 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]  Gavruta, 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]  Gilányi, A. (2002) On a Problem by K. Nikodem. Mathematical Inequalities & Applications, 5, 707-710.
[7]  Prager, W. and Schwaiger, J. (2013) A System of Two Inhomogeneous Linear Functional Equations. Acta Mathematica Hungarica, 140, 377-406. https://doi.org/10.1007/s10474-013-0315-y
[8]  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
[9]  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
[10]  Park, C. (2015) Additive ρ-Functional Inequalities and Equations. Journal of Mathematical Inequalities, 9, 17-26.
[11]  Park, C. (2015) Additive ρ-Functional Inequalities in Non-Archimedean Normed Spaces. Journal of Mathematical Inequalities, 9, 397-407.
[12]  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
[13]  Fechner, W. (2010) On Some Functional Inequalities Related to the Logarithmic Mean. Acta Mathematica Hungarica, 128, 36-45. https://doi.org/10.1007/s10474-010-9153-3
[14]  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.
[15]  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
[16]  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
[17]  Yun, S. and Shin, D.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
[18]  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
[19]  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
[20]  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
[21]  Gilányi, A. (2002) Eine zur parallelogrammleichung äquivalente ungleichung. Aequations, 5, 707-710.*
[22]  Qarawani, M. (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 https://www.scirp.org/journal/am/
[23]  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 No. 41820. https://doi.org/10.1155/2007/41820
[24]  Rätz, J. (2003) On Inequalities Assosciated with the Jordan-Von Neumann Functional Equation. Aequationes Matheaticae, 66, 191-200. https://doi.org/10.1007/s00010-003-2684-8
[25]  Van An, L.Y. (2022) Generalized Hyers-Ulam-Rassisa Stabilityof an Additive (1; 2)-Functional Inequalities with nVariables in Complex Banach. Open Access Library Journal, 9, e9183. https://doi.org/10.4236/oalib.1109183
[26]  Van An, L.Y. (2019) Hyers-Ulam Stability of Functional Inequalities with Three Variable in Banach Spaces and Non-Archemdean Banach Spaces. International Journal of Mathematical Analysis, 13, 519-537. https://doi.org/10.12988/ijma.2019.9954
[27]  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

Full-Text


Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133