GENERALIZED HYERS-ULAM -RASSISA STABILITY OF AN ADDITIVE β1, β2 -FUNCTIONAL INEQUALITIES WITH THREE VARIABLES IN COMPLEX BANACH SPACE
Keywords:
Additive β1, β2 -functional inequality, fixed point method; direct method, Banach space, Hyers Ulam stability
Abstract
In this paper we study to solve the of additive β1, β2 -functional inequality with three 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. I will show that the solutions of the additive β1, β2 - functional inequality are additive mapping. T hen Hyers Ulam stability of these equation are given and proven. T hese are the main results of this paper.
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References
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[2] A.Bahyrycz, M. Piszczek, Hyers stability of the Jensen function equation, Acta Math. Hungar.,142
(2014),353-365. .
[3] Ly V an An. Hyers-Ulam stability of functional inequalities with three variable in Banach spaces and Non-Archemdean Banach spaces International Journal of Mathematical Analysis Vol.13, 2019, no. 11. 519-53014), 296-310. .https://doi.org/10.12988/ijma.2019.9954.
[4] Ly V an An. Hyers-Ulam stability of β-functional inequalities with three variable in non-Archemdean
Banach spaces and complex Banach spaces International Journal of Mathematical Analysis Vol. 14, 2020, no. 5, 219 - 239 .HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2020.91169.
.https://doi.org/10.12988/ijma.2019.9954
[5] M.Balcerowski, On the functional equations related to a problem of z Boros and Z. Dro´czy, Acta Math. Hungar.,138 (2013), 329-340. .
[6] L. CADARIU ? , V. RADU, Fixed points and the stability of Jensens functional equation, J. Inequal. Pure Appl. Math. 4, no. 1, Art. ID 4 (2003). .
[7] J. DIAZ, B. MARGOLIS, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Am. Math. Soc. 74 (1968), 305-309. .
[8] W Fechner, On some functional inequalities related to the logarithmic mean, Acta Math., Hungar., 128 (2010,)31-45, 303-309 . . .
[9] W. Fechner, Stability of a functional inequlities associated with the Jordan-von Neumann functional equation, Aequationes Math. 71 (2006), 149-161
[10] Pascus. Ga˘vruta, A generalization of the Hyers-Ulam -Rassias stability of approximately ad- ditive mappings, Journal of mathematical Analysis and Aequations 184 (3) (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211 .
[11] Attila Gila´nyi, On a problem by K. Nikodem, Math. Inequal. Appl., 5 (2002), 707-710. . .
[12] Attila Gila´nyi, Eine zur parallelogrammleichung a¨quivalente ungleichung, Aequations 5 (2002),707- 710. https: //doi.org/ 10.7153/mia-05-71 .
[13] Donald H. Hyers, On the stability of the functional equation, Proceedings of the National Academy of the United States of America,
27 (4) (1941), 222.https://doi.org/10.1073/pnas.27.4.222,
[14] Jung Rye Lee, Choonkil Park, and DongY unShin. Additive and quadratic functional in equalities in Non-Archimedean normed spaces, International Journal of Mathematical Analysis, 8 (2014), 1233- 1247.. .https://doi.org/10.12988/ijma.2019.9954.
[15] L. Maligranda. Tosio Aoki (1910-1989). In International symposium on Banach and function spaces: 14/09/2006-17/09/2006, pages 1–23. Yokohama Publishers, 2008.
[16] D. MIHET, V. RADU, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), 567-572.
[17] A. Najati and G. Z. Eskandani. Stability of a mixed additive and cubic functional equation in quasi- Banach spaces. J. Math. Anal. Appl., 342(2):1318–1331, 2008.
[18] C. Park,Y. Cho, M. Han. Functional inequalities associated with Jordan-von Newman-type additive functional equations , J. Inequality .Appl. ,2007(2007), Article ID 41820, 13 pages.. .
.
[19] W. P and J. Schwaiger, A system of two in homogeneous linear functional equations, Acta Math. Hungar 140 (2013), 377-406 . .
[20] Ju¨rg Ra¨tz On inequalities assosciated with the jordan-von neumann functional equation, Aequationes matheaticae, 66 (1) (2003), 191-200 https;// doi.org/10-1007/s00010-0032684-8. .
[21] Choonkil. Park. the stability an of additive (p1, p2)-functional inequality in Banach spaceJournal of mathematical Inequalities Volume 13, Number 1 (2019), 95-104. .
[22] Choonkil. Park. Additive β-functional inequalities, Journal of Nonlinear Science and Appl. 7(2014), 296-310. .
[23] Choonkil Park,. functional in equalities in Non-Archimedean normed spaces. Acta Mathematica
Sinica, English Series, 31 (3), (2015), 353-366. .https://doi.org/10.1007/s10114-015-4278-5
[24] C. PARK, Additive ρ-functional inequalities and equations, J. Math. Inequal. 9 (2015), 17-26. .
[25] C. PARK, Additive ρ-functional inequalities in non-Archimedean normed spaces, J. Math. Inequal. 9 (2015), 397-407 .
[26] Themistocles M. Rassias, On the stability of the linear mapping in Banach space, proceedings of the American Mathematical Society, 27 (1978), 297-300. https: //doi.org/10.2307 /s00010-003-2684-8 .
.
[27] F. SKOF, Propriet locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53 (1983),113-
129. .
[28] S M. ULam. A collection of Mathematical problems, volume 8, Interscience Publishers. New York,1960.
Published
2022-09-22
How to Cite
VAN AN, L. (2022). GENERALIZED HYERS-ULAM -RASSISA STABILITY OF AN ADDITIVE β1, β2 -FUNCTIONAL INEQUALITIES WITH THREE VARIABLES IN COMPLEX BANACH SPACE. IJRDO -JOURNAL OF MATHEMATICS, 8(9), 1-14. https://doi.org/10.53555/m.v8i9.5269
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