GENERALIZED ESTABLISH JENSEN TYPE ADDITIVE λ1; λ2-FUNCTIONAL INEQUALITIES WITH 3k-VARIABLES IN α1; α2-HOMOGENEOUS F-SPACES
DOI:
https://doi.org/10.53555/ms.v9i3.2211Keywords:
Complex Banach space, Hyers-Ulam-Rassias stability, Additive (λ1, λ2)-Functional Inequalities, (α1,α2)-Homogeneous F spacesAbstract
In this paper, we study to solve two additive λ1; λ2-functional inequalities
with 3k-variables in α1; α2-homogeneous F spaces. Then we will show that the solutions of the first and second inequalities are additive mappings.That is the main result
in this paper.
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References
ULam, S.M. (1960) A Collection of Mathematical Problems. Vol. 8, Interscience Publishers, New
York.
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.
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.
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.
G˘ avruta, 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.
Gil´ anyi, A. (2002) On a Problem by K. Nikodem. Mathematical Inequalities Applications, 5, 707-710.
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.
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-
-9.
Park, C. (2014) Additive β-Functional Inequalities. Journal of Nonlinear Sciences and Applications,
, 296-310. https://doi.org/10.22436/jnsa.007.05.02
Park, C. (2015) Additive η-Functional Inequalities and Equations. Journal of Mathematical Inequalities, 9, 17-26.
Park, C. (2015) Additive β-Functional Inequalities in Non-Archimedean Normed Spaces. Journal of
Mathematical Inequalities, 9, 397-407.
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
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
Cadariu, L. and Radu, V. (2003) Fixed Points and the Stability of Jensens Functional Equation.
Journal of Inequalities in Pure and Applied Mathematics, 4, Article No. 4.
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
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
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
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. Dr.
Acta Mathematica Hungarica, 138, 329-340. https://doi.org/10.1007/s10474-012-0278-4
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/
Park, C., Cho, Y. and Han, M. (2007) Functional Inequalities Associated with Jordan-Von NewmanType Additive Functional Equations. Journal of Inequalities and Applications, 2007, Article No.
https://doi.org/10.1155/2007/41820
R, 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
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
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,
-537. https://doi.org/10.12988/ijma.2019.9954
Van An, LY. (2020) Hyers-Ulam Stability of Functional Inequalities with Three Variable in NonArchemdean Banach Spaces and Complex Banach. International Journal of Mathematical Analysis,
, 219-239. https://doi.org/10.12988/ijma.2020.91169
Ly Van An Generalized Stability of Functional Inequalities with 3k-Variables Associated for Jordan-von Neumann-Type Additive Functional Equation Open Access Library
Journal.Open Access Library Journal 2023, Volume 10, e9681 ISSN Online: 2333-9721
https://doi.org/10.4236/oalib.1109681 ISSN Print: 2333-9705 Vol.10 No.1, January 2023
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