Generalized Hyers-Ulam-Rassisa Stability of An Additive (β1,β2)-Functional Inequalities With n- Variables In Complex Banach Space
DOI:
https://doi.org/10.14419/gjma.v10i1.32143الكلمات المفتاحية:
Additive (β1، β2)-functional inequality، fixed point method، direct method، Banach space، Hyers−Ulam stability.الملخص
In this paper we study to solve the o f additive (β1,β2)-f unctional 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. I will show that the solutions of the additive (β1,β2)-f unctional inequality are additive mapping. Then Hyers−Ulam stability o f these equation are given and proven. T hese are the main results o f this paper .
المراجع
[1] T.Aoki, On the stability of the linear transformation in Banach space, J. Math. Soc. Japan 2(1950), 64-66.
[2] A.Bahyrycz, M. Piszczek, Hyers stability of the Jensen function equation, Acta Math. Hungar.,142 (2014),353-365.
[3] Ly Van 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 Van An, Hyers-Ulam stability of β-functional inequalities with three variable in non-Archemdean Banach spaces and complex Banach spaces Inter-
national 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. Dr Ìoczy, Acta Math. Hungar.,138 (2013), 329-340.
[6] L. CADARIU ? , V. RADU, Fixed points and the stability of Jensen’s 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 additive mappings, Journal of mathematical Analysis and
Aequations 184 (3) (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211.
[11] Attila Gil Ìanyi, On a problem by K. Nikodem, Math. Inequal. Appl., 5 (2002), 707-710.
[12] Attila Gil Ìanyi, Eine zur parallelogrammleichung ̈aquivalente 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 Dong Yun Shin. 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). 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] Jurg ̈ 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 (β1,β2
-functional inequality in Banach space
Journal 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 Ï-functional inequalities and equations, J. Math. Inequal. 9 (2015), 17-26.
[25] C. PARK, Additive Ï-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.
التنزيلات
منشور
إصدار
القسم
الرخصة
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal''s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
