GENERALIZED HYERS-ULAM-RASSIAS TYPE STABILITY OF THE 2k-VARIABLE ADDITIVE FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN BANACH SPACES AND BANACH SPACES

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-9
Year of Publication : 2021
Authors : LY VAN AN
  10.14445/22315373/IJMTT-V67I9P521

MLA

MLA Style: LY VAN AN. "GENERALIZED HYERS-ULAM-RASSIAS TYPE STABILITY OF THE 2k-VARIABLE ADDITIVE FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN BANACH SPACES AND BANACH SPACES" International Journal of Mathematics Trends and Technology 67.9 (2021):183-197. 

APA Style: LY VAN AN(2021). GENERALIZED HYERS-ULAM-RASSIAS TYPE STABILITY OF THE 2k-VARIABLE ADDITIVE FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN BANACH SPACES AND BANACH SPACES  International Journal of Mathematics Trends and Technology, 67(9), 183-197.

Abstract
In this paper we use the direct method to proved two the generalized additive functional inequalities with 2k-variables and their Hyers-Ulam-Rassias stability. First are investigated in Banach spaces and the last are investigated in non-Archimedean Banach spaces. We will show that the solutions of the inequalities are additive mappings. These are the main results of this paper.

Reference

[1] Tosio Aoki. On the stability of the linear transformation in banach spaces. Journal of the Mathe- matical Society of Japan, 2(1-2):64{66, 1950.
[2] 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. .
[3] A.Bahyrycz, M. Piszczek, Hyers stability of the Jensen function equation, Acta Math. Hungar.,142 (2014),353-365. .
[4] M.Balcerowski, On the functional equations related to a problem of z Boros and Z. Droczy, Acta Math. Hungar.,138 (2013), 329-340.
[5] H:Dimou1; Y:ribou2; S:Kabbaj3. Generalzed functional inequalities in Banach space,Volume 7(2), 202, Pages 337-349.. .ISSN:Online 2351-8227-Print 2605-6364.DOI:10.2478/mjpaa-2021-0022.
[6] W lodzimierz Fechner. Stability of a functional inequality associated with the jordan{von neumann functional equation. Aequationes Mathematicae, 71(1):149{161, 2006.
[7] Pascu Gavruta A generalization of the hyers-ulam-rassias stability of approximately additive mappings. Journal of Mathematical Analysis and Applications, 184(3):431{436, 1994.
[8] Attila Gilanyi. Eine zur parallelogrammgleichung aquivalente ungleichung. Aequationes Mathemati- cae, 62(3):303{309, 2001. GENERALIZED HYERS-ULAM-RASSIAS TYPE STABILITY OF THE 2k-VARIABLE ADDITIVE FUNCTIONAL INEQUALITIES [9] Attila Gilanyi. On a problem by k. nikodem. Mathematical Inequalities and Applications, 5:707{710, 2002.
[10] Donald H Hyers. On the stability of the linear functional equation. Proceedings of the National Academy of Sciences of the United States of America, 27(4):222, 1941.
[11] . K. Hensel, Uber eine neue Begrundung der Theorie der algebraischen Zahlen, Jahres-ber Deutsch. Math. Verein, 6(1897), 8388 .
[12] Jung Rye Lee, Choonkil Park, and Dong Yun Shin. Additive and quadratic functional in equalities in non-archimedean normed spaces. 2014.
[13] M.S. Moslehian and M.Th. Rassias, Stability of functional equations in non-Archimedean spaces, Appl. Anal. Discrete Math, 1 (2007), 325334. .
[14] W. P and J. Schwaiger, A system of two inhomogeneous linear functional equations, Acta Math. Hungar 140 (2013), 377-406 .
[15] Choonkil Park. Functional inequalities in non-archimedean normed spaces. Acta Mathematica Sinica, English Series, 31(3):353{366, 2015.
[16] Choonkil Park, Young Sun Cho, and Mi-Hyen Han. Functional inequalities associated with jordan-von neumann-type additive functional equations. Journal of Inequalities and Applications, 2007(1):041820, 2006.
[17] Choonkil: Park. Additive β-functional inequalities, Journal of Nonlinear Science and Appl. 7(2014), 296-310 .
[18] Choonkil: Park. Additive ρ-functional inequalities and equations, Journal of Mathmatical inequali- ties Volum 9, Number 1 (2015), 17- 26 doi: 10.7153/jmi-09-02. .
[19] Themistocles M Rassias. On the stability of the linear mapping in banach spaces. Proceedings of the American Mathematical Society, 72(2):297{300, 1978.
[20] Jurg Ratz. On inequalities associated with the jordan-von neumann functional equation. Aequationes mathematicae, 66(1):191{200, 2003.
[21] Stanislaw M Ulam. A collection of mathematical problems, volume 8. Interscience Publishers, 1960.

Keywords : Cauchy functional equation, additive functional inequality, additive β - functional inequalities, Banach space, non-Archimedian Banach space, Hyers-Ulam-Rassias stability.