ESTABLISH AN ADDITIVE (s;t)-FUNCTION IN EQUALITIES BY FIXED POINT METHOD AND DIRECT METHOD WITH n-VARIABLES IN BANACH SPACE
Keywords:
Additive s, t -functional inequality, fixed point method, direct method, Banach space, Hyers Ulam stability
Abstract
In this paper we study to solve the of additive s, t -functional inequality with n-variables and their Hyers-Ulam stability. First are investigated in Banach spaces with a fixed point method and last are investigated in Banach spaces with a direct method.These 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
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[24] Hungar 140 (2013), 377-406
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[26] Choonkil. Park. the stability an of additive (β1, β2 -functional inequality in Banach spaceJournal of mathematical Inequalities Volume 13, Number 1 (2019), 95-104. .
[27] Choonkil. Park. Additive β-functional inequalities, Journal of Nonlinear Science and Appl. 7(2014), 296-310. .
[28] Choonkil Park,. functional in equalities in Non-Archimedean normed spaces. Acta Mathematica
[29] Sinica, English Series, 31 (3), (2015), 353-366. .https://doi.org/10.1007/s10114-015-4278-5
[30] C. PARK, Additive ρ-functional inequalities and equations, J. Math. Inequal. 9 (2015), 17-26. .
[31] C. PARK, Additive ρ-functional inequalities in non-Archimedean normed spaces, J. Math. Inequal. 9 (2015), 397-407 .
[32] 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 .
[33] .
[34] F. SKOF, Propriet locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53 (1983),113-
[35] 129. .
[36] S M. ULam. A collection of Mathematical problems, volume 8, Interscience Publishers. New York,1960.
[37] Corresponding Author: Ly Van An.
[2] A.Bahyrycz, M. Piszczek, Hyers stability of the Jensen function equation, Acta Math. Hungar.,142
[3] (2014),353-365. .
[4] 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.
[5] 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.
[6] .https://doi.org/10.12988/ijma.2019.9954
[7] An, L.V. (2022) Generalized Hyers-Ulam-Rassisa Stability of an Additive β1, β2 -Functional In- equalities with n-Variables in Complex Banach Space. Open Access Library Journal, 9, e9183. https://doi.org/10.4236/oalib.1109183.
[8] M.Balcerowski, On the functional equations related to a problem of z Boros and Z. Dro´czy, Acta Math. Hungar.,138 (2013), 329-340. .
[9] 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). .
[10] 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. .
[11] W Fechner, On some functional inequalities related to the logarithmic mean, Acta Math., Hungar., 128 (2010,)31-45, 303-309 . . .
[12] W. Fechner, Stability of a functional inequlities associated with the Jordan-von Neumann functional equation, Aequationes Math. 71 (2006), 149-161
[13] 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 .
[14] Attila Gila´nyi, On a problem by K. Nikodem, Math. Inequal. Appl., 5 (2002), 707-710. . .
[15] Attila Gila´nyi, Eine zur parallelogrammleichung a¨quivalente ungleichung, Aequations 5 (2002),707- 710. https: //doi.org/ 10.7153/mia-05-71 .
[16] Donald H. Hyers, On the stability of the functional equation, Proceedings of the National Academy of the United States of America,
[17] 27 (4) (1941), 222.https://doi.org/10.1073/pnas.27.4.222,
[18] 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.
[19] 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.
[20] 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.
[21] 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.
[22] 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.. .
[23] W. P and J. Schwaiger, A system of two in homogeneous linear functional equations, Acta Math.
[24] Hungar 140 (2013), 377-406
[25] 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. .
[26] Choonkil. Park. the stability an of additive (β1, β2 -functional inequality in Banach spaceJournal of mathematical Inequalities Volume 13, Number 1 (2019), 95-104. .
[27] Choonkil. Park. Additive β-functional inequalities, Journal of Nonlinear Science and Appl. 7(2014), 296-310. .
[28] Choonkil Park,. functional in equalities in Non-Archimedean normed spaces. Acta Mathematica
[29] Sinica, English Series, 31 (3), (2015), 353-366. .https://doi.org/10.1007/s10114-015-4278-5
[30] C. PARK, Additive ρ-functional inequalities and equations, J. Math. Inequal. 9 (2015), 17-26. .
[31] C. PARK, Additive ρ-functional inequalities in non-Archimedean normed spaces, J. Math. Inequal. 9 (2015), 397-407 .
[32] 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 .
[33] .
[34] F. SKOF, Propriet locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53 (1983),113-
[35] 129. .
[36] S M. ULam. A collection of Mathematical problems, volume 8, Interscience Publishers. New York,1960.
[37] Corresponding Author: Ly Van An.
Published
2023-01-07
How to Cite
LYVANAN. (2023). ESTABLISH AN ADDITIVE (s;t)-FUNCTION IN EQUALITIES BY FIXED POINT METHOD AND DIRECT METHOD WITH n-VARIABLES IN BANACH SPACE. IJRDO -JOURNAL OF MATHEMATICS, 9(1), 1-13. https://doi.org/10.53555/m.v9i1.5515
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