STABILITY OF FUNCTIONAL INEQUALITIES WITH 3K-VARIABLE BASED ON JORDAN-VON NEUMANN TYPE ADDITIVE FUNCTIONAL EQUATIONS IN BANACH SPACE

Authors

  • LY VAN AN Faculty of Mathematics Teacher Education, Tay Ninh University, Tay Ninh, Vietnam.

DOI:

https://doi.org/10.53555/ms.v9i1.2201

Keywords:

Normed Spaces, Banach Space, Generalized Hyers-Ulam-Rassias Stabil- ity Jordan-von Neumann-Type Additive Functional Equation, Cauchy, Jensen Additive Function Inequalities

Abstract

 In this paper, we study to solve the Cauchy, Jensen and Cauchy-Jensen additive function inequalities with 3k-variables related to Jordan-von Neumann type in Banach space. These are the main results of this paper.

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References

S.M. ULam A collection of Mathematical problems, volume 8, Interscience Publishers. New York,1960.

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,

Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proceedings of the American Mathematical Society, vol.72,no.2,pp.297-300,1978.

Z. Gajda, On stability of additive mappings, International Journal of Mathematics and Mathematical Sciences, vol.14,no.3,pp.431-434,1991.

S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, USA, 2002.

P. Ga˘vrut, ”A generalization of the Hyers-Ulam-Rassias stability of approximately additive map- pings,” Journal of Mathematical Analysis and Applications, vol.184,no.3,pp.431-436,1994.

A. Gila´nyi, Eine zur Parallelogrammgleichung aquivalente Ungleichung, Aequationes Mathematicae,

vol.62,no.3,pp.303-309,2001.

Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proceedings of the American Mathematical Society, vol.114,no.4,pp.989-993,1992.

D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, vol. 34 of Progress in Nonlinear Differential Equations and Their Applications, Birkhauser Boston, Boston, Mass, USA, 1998.

J. M. Rassias, On approximation of approximately linear mappings by linear mappings, Journal of Functional Analysis, vol.46,no.1,pp.126-130,1982.

K.-W. Jun and Y.-H. Lee, A generalization of the Hyers-Ulam-Rassias stability of the pexiderized quadratic equations, Journal of Mathematical Analysis and Applications, vol.297,no.1,pp.7086, 2004.

S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, Fla, USA, 2001.

C. Park, Homomorphisms between Poisson JC-algebras, Bulletin of the Brazilian Mathematical Society. New Series, vol.36,no.1,pp.79-97,2005.

C. Park, Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras to appear in Bulletin des Sciences Mathematiques.

Th. M. Rassias, Problem 16; 2, Report of the 27th International Symp. on Functional Equations, Aequationes Mathematicae, vol.39,pp.292-93;309,1990

J. Ratz, On inequalities associated with the Jordan-von Neumann functional equation, Aequationes Mathematicae, vol.66,no.1-2,pp.191-200,2003.ChoonkilParketal.13

A. Gila’nyi, On a problem by K. Nikodem,Mathematical Inequalities Applications, vol. 5, no. 4, pp. 707-710, 2002.

T.Aoki, On the stability of the linear transformation in Banach space, J. Math. Soc. Japan 2(1950), 64-66.

A.Bahyrycz, M. Piszczek, Hyers stability of the Jensen function equation, Acta Math. Hungar.,142 (2014),353-365.

M.Balcerowski, On the functional equations related to a problem of z Boros and Z. Dro´czy, Acta Math. Hungar.,138 (2013), 329-340.

W. Fechner, Stability of a functional inequlities associated with the Jordan-von Neumann functional equation, Aequationes Math. 71 (2006), 149-161.

W. P and J. Schwaiger, A system of two inhomogeneous linear functional equations, Acta Math. Hungar 140 (2013), 377-406.

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.

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.

Attila Gila´nyi, On a problem by K. Nikodem, Math. Inequal. Appl., 5 (2002), 707-710.

W Fechner, On some functional inequalities related to the logarithmic mean, Acta Math., Hungar., 128 (2010,)31-45, 303-309.

Choonkil.Park. Additive β-functional inequalities, Journal of Nonlinear Science and Appl. 7(2014), 296-310.

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.

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.

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.

Y.J.Choa, Choonkil Parkb∗, and R.Saadatic,b∗ functional in equalities in Non-Archimedean normed spaces, Applied Mathematics Letters 23(2010), 1238-1242.

Y.Aribou∗, S.Kabbaj Generalized functional in inequalities in Non-Archimedean normed spaces, Applied Mathematics Letters 2, (2018) Pages: 61-66.

LY VAN AN, Hyers-Ulam stability additive β-functional inequalities with three variable in Banach spaces and Non-Archemdean Banach spaces International Journal of Mathematical Analysis Vol.14, 2020, no. 5-8. 519-53014, 296-310 .https://doi.org/10.12988/ijma.2020.91169.

LY VAN AN,Generalized Hyes-Ulam stability of the additive functional inequalities with 2n- varables in non–Archimedean Banach space. Bulletin of mathematics and statistics research. Vol.9.Issue.3.2021 (July-Sept) Ky publications .http//www.bomsr.comDOI:10.33329/bomsr.9.3. 67.

, Qarawani, M.N. (2013), Hyers-Ulam-Rassias Stability for the Heat Equation, Applied Mathematics, Vol. 4 No. 7, 2013, pp. 1001-1008. doi:10.4236/am.2013.47137.

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Published

2023-02-04

How to Cite

AN, L. V. . (2023). STABILITY OF FUNCTIONAL INEQUALITIES WITH 3K-VARIABLE BASED ON JORDAN-VON NEUMANN TYPE ADDITIVE FUNCTIONAL EQUATIONS IN BANACH SPACE. International Journal For Research In Mathematics And Statistics, 9(1). https://doi.org/10.53555/ms.v9i1.2201