Hyers-Ulam-Rassias Stability of the \(C^*\)-ternary Bi-homomorphisms and \(C^*\)-ternary Bi-derivations in \(C^*\)-ternary Algebras

Authors

  • Prondanai Kaskasem Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000
  • Chakkrid Klin-eam Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok 65000

DOI:

https://doi.org/10.26713/cma.v10i4.1249

Keywords:

Hyers-Ulam-Rassias stability, \(C^*\)-ternary bi-homomorphisms, \(C^*\)-ternary bi-derivations, \(C^*\)-ternary algebras

Abstract

In this  paper, we prove Hyers-Ulam-Rassias stability of \(C^*\)-ternary bi-homomorphisms and \(C^*\)-ternary bi-derivations in \(C^*\)-ternary algebras by using alternative fixed point theorem.

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References

V. Abramov, R. Kerner and B. L. Roy, Hypersymmetry: a Z3-graded generalization of supersymmetry, J. Math. Phys. 38 (1997), 1650 – 1669, DOI: 10.1063/1.531821.

J. H. Bae and W. G. Park, Approximate bi-homomorphisms and bi-derivations in C*-ternary algebras, Bull. Korean Math. Soc. 47(1) (2010), 195 – 209, DOI: 10.4134/BKMS.2010.47.1.195.

J. A. Baker, The stability of certain functional equations, Proc. Am. Math. Soc. 112 (1991), 729 – 732, DOI: 10.1090/S0002-9939-1991-1052568-7.

J. Brzde¸k, W. Fechner, M. S. Moslehian and J. Silorska, Recent developments of the conditional stability of the homomorphism equation, Banach J. Math. Anal. 9(3) (2015), 278 – 326, DOI: 10.15352/bjma/09-3-20.

J. Brzde¸k, D. Popa, I. Rasa and B. Xu, Ulam Stability of Operators: Mathematical Analysis and its Applications, Vol. 1, Academic Press, Elsevier, Oxford (2018), https://www.elsevier.com/books/ulam-stability-of-operators/brzdek/978-0-12-809829-5.

Y. J. Cho, C. Park, Th. M. Rassias and R. Saadati, Stability of functional equations in Banach Algebras, Springer International Publishing Switzerland, (2015), DOI: 10.1007/978-3-319-18708-2.

Y. J. Cho, Th. M. Rassias and R. Saadati, Stability of Functional Equations in Random Normed Spaces, Springer Scienceí…Business Media New York, (2013), DOI: 10.1007/978-1-4614-8477-6.

J. B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74(2) (1968), 305 – 309, https://projecteuclid.org/euclid.bams/1183529535.

P. G˘avru¸ta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mapping, J. Math. Anal. Appl. 184 (1994), 431 – 436, DOI: 10.1006/jmaa.1994.1211.

M. E. Gordji and S. Abbaszadeh, Theory of Approximate Functional Equations in Banach Algebras, Inner Product Spaces and Amenable Groups, Academic Press, (2016), https://www.elsevier.com/books/theory-of-approximate-functional-equations/gordji/978-0-12-803920-5.

D. H. Hyers, On the stability of the linear functional equation, Proc. N.A.S. USA 27 (1941), 222 – 224, DOI: 10.1073/pnas.27.4.222.

S. M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Science+Business Media LLC, (2010), DOI: 10.1007/978-1-4419-9637-4.

R. Kerner, Ternary algebraic structures and their applications in physics, Preprint: arXiv:mathph/0011023 (2000), https://arxiv.org/abs/math-ph/0011023.

W. A. J. Luxemburg, On the covergence of successive approximations in the theory of ordinary differential equations, II Koninkl, Nederl. Akademie van Wetenschappen, Amsterdam, Proc. Ser. A (5) 61, Indag. Math., 20 (1958), 540 – 546, https://core.ac.uk/download/pdf/82153342.pdf.

C. Park, Bi-additive s-functional inequalities and quasi-¤-multipliers on Banach algebras, Mathematics 6(3) (2018), DOI: 10.3390/math6030031, DOI: 10.3390/math6030031.

C. Park, C*-ternary biderivations and C*-ternary bihomomorphisms, Mathematics 6(3) (2018), DOI: 10.3390/math6030030, DOI: 10.3390/math6030030.

W. G. Park and J. H. Bae, A fixed point approach to the stability of a functional equation, Kyungpook Math. J. 50 (2010), 557 – 564, DOI: 10.5666/KMJ.2010.50.4.557.

W. G. Park and J. H. Bae, A functional equation related to quadratic forms without the cross product terms, Honam Math. J. 30 (2008), 219 – 225, DOI: 10.5831/HMJ.2008.30.2.219.

W. G. Park and J. H. Bae, Stability of bi-additive functional equation in banach modules over a C*-algebra, Discrete Dyn. Nat. Soc. Vol. 2012, Article ID 835893, DOI: 10.1155/2012/835893.

V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), 91 – 96, https://pdfs.semanticscholar.org/07a5/2215aba879ec342dd50a8a8dbafc7c461d5d.pdf.

J. M. Rassias, E. Thandapani, K. Ravi and B. V. Senthil Kumar, Functional Equations and Inequalities: Solutions and Stability Results, World Scientific Publishing, (2017), DOI: 10.1142/9789813147614_0001.

Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297 – 300, DOI: 10.1090/S0002-9939-1978-0507327-1.

S. M. Ulam, A collection of mathematical problems, Intersci. Tracts. in Pure and Appl. Math., No. 8, Intersci. Publishers, New York, USA (1960), https://books.google.co.in/books/about/A_Collection_of_Mathematical_Problems.html?id=u_kHAAAAMAAJ&redir_esc=y.

L. Vainerman and R. Kerner, On special classes of n-algebras, J. Math. Phys. 37 (1996), 2553 – 2565, DOI: 10.1063/1.531526.

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Published

31-12-2019
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How to Cite

Kaskasem, P., & Klin-eam, C. (2019). Hyers-Ulam-Rassias Stability of the \(C^*\)-ternary Bi-homomorphisms and \(C^*\)-ternary Bi-derivations in \(C^*\)-ternary Algebras. Communications in Mathematics and Applications, 10(4), 821–843. https://doi.org/10.26713/cma.v10i4.1249

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Research Article