Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


Covered by:
Web of Science - Emerging Sources Citation Index
Scopus
MathSciNet


CiteScore 2018: 0.47
SCImago Journal Rank (SJR) 2018: 0.265
Source Normalized Impact per Paper (SNIP) 2018: 0.714

Mathematical Citation Quotient (MCQ) 2018: 0.17

ICV 2018: 121.16

Open Access
Online
ISSN
2391-4661
See all formats and pricing
More options …
Volume 51, Issue 1

Issues

Approximation of additive functional equations in NA Lie C*-algebras

Zhihua Wang / Reza Saadati
Published Online: 2018-04-13 | DOI: https://doi.org/10.1515/dema-2018-0003

Abstract

In this paper, by using fixed point method, we approximate a stable map of higher *-derivation in NA C*-algebras and of Lie higher *-derivations in NA Lie C*-algebras associated with the following additive functional equation

,

where m ≥ 2.

Keywords: Fixed point method; approximation; higher *-derivations; Lie higher *-derivations; non-Archimedean Lie C*-algebras

MSC 2010: 39B82; 39B52; 16W25; 46L05; 47H10

References

  • [1] Najati A., Eskandani G. Z., Stability of derivations on proper Lie CQ*-algebras, Commun. Korean Math. Soc., 2009, 24, 5-16CrossrefGoogle Scholar

  • [2] Jung S.-M., Nam Y. W., Hyers-Ulam stability of Pielou logistic difference equation, J. Nonlinear Sci. Appl., 2017, 10, 3115-3122Google Scholar

  • [3] Lu G., Xie J., Liu Q., Jin Y., Hyers-Ulam stability of derivations in fuzzy Banach space, J. Nonlinear Sci. Appl., 2016, 9, 5970- 5979CrossrefGoogle Scholar

  • [4] Abdou A., Cho Y. J., Saadati R., Distribution and survival functions with applications in intuitionistic random Lie C*-algebras, J. Comput. Anal. Appl., 2016, 21, 345-354Google Scholar

  • [5] Cho Y. J., Saadati R., Vahidi J., Approximation of homomorphisms and derivations on non-Archimedean Lie C*-algebras via fixed point method, Discrete Dyn. Nat. Soc., 2012, art. ID 373904Google Scholar

  • [6] Jang S. Y., Saadati R., Approximation of the Jensen type functional equation in non-Archimedean C*-algebras, J. Comput. Anal. Appl., 2015, 18, 472-491Google Scholar

  • [7] Kang J. I., Saadati R., Approximation of homomorphisms and derivations on non-Archimedean random Lie C*-algebras via fixed point method, J. Ineq. Appl., 2012, art. ID 251Google Scholar

  • [8] Moslehian M. S., Sadeghi G., A Mazur-Ulam theorem in non-Archimedean normed spaces, Nonlinear Anal., 2008, 69, 3405- 3408Google Scholar

  • [9] Ghaemi M. B., Choubin M., Saadati R., Park C., Shin D. Y., A fixed point approach to the stability of Euler-Lagrange sextic (a, b)-functional equations in Archimedean and non-Archimedean Banach spaces, J. Comput. Anal. Appl., 2016, 21, 170-181Google Scholar

  • [10] Shilkret N., Non-Archimedean Banach algebras, PhD thesis, Polytechnic University, ProQuest LLC, 1968Google Scholar

  • [11] Diaz J. B., Margolis B., A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 1968, 74, 305-309Google Scholar

  • [12] Alsulami H. H., Kenari H. M., O’Regan D., Saadati R., Multi-C*-ternary algebras and applications, J. Inequal. Appl., 2015, 2015:223Google Scholar

  • [13] Cho Y. J., Park C., Rassias T. M., Saadati R., Stability of functional equations in Banach algebras, Springer, Cham, 2015Google Scholar

  • [14] Agarwal R. P., Saadati R., Salamati A., Approximation of the multiplicatives on random multi-normed space, J. Inequal. Appl., 2017, 2017:204CrossrefWeb of ScienceGoogle Scholar

  • [15] Alshybani S., Vaezpour S. M., Saadati R., Generalized Hyers-Ulam stability of mixed type additive-quadratic functional equation in random normed spaces, J. Math. Anal., 2017, 8, 12-26Google Scholar

  • [16] Aoki T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 1950, 2, 64-66Google Scholar

  • [17] Bahyrycz A., Brzdęk J., Jablońska E., Olko J., On functions that are approximate fixed points almost everywhere and Ulam’s type stability, J. Fixed Point Theory Appl., 2015, 17, 659-668Web of ScienceGoogle Scholar

  • [18] Cho Y. J., Saadati R., Yang Y.-O., Kenari H. M., A fixed point technique for approximate a functional inequality in normed modules over C*-algebras, Filomat 2016, 30, 1691-1696Web of ScienceGoogle Scholar

  • [19] De la Sen M., O’Regan D., Saadati R., Characterization of modular spaces, J. Comput. Anal. Appl., 2017, 22, 558-572Google Scholar

  • [20] Găvruță P., A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 1994, 184, 431-436Google Scholar

  • [21] Hyers D. H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 1941, 27, 222-224Google Scholar

  • [22] Hyers D. H., Isac G., Rassias Th. M., Stability of Functional Equations in Several variables, Birkhäuser, Basel, 1998Web of ScienceGoogle Scholar

  • [23] Kannappan P., Functional Equations and Inequalities with Applications, Springer Science, New York, 2009Google Scholar

  • [24] Kim S. O., Bodaghi A., Park C., Stability of functional inequalities associated with the Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces, J. Nonlinear Sci. Appl., 2015, 8, 776-786Google Scholar

  • [25] Naeem R., Anwar M., Jessen type functionals and exponential convexity, J. Math. Computer Sci., 2017, 17, 429-436CrossrefGoogle Scholar

  • [26] Pansuwan A., Sintunavarat W., Choi J. Y., Cho Y. J., Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problems in M-metric spaces, J. Nonlinear Sci. Appl., 2016, 9, 4489-4499CrossrefGoogle Scholar

  • [27] Park C., Anastassiou G. A., Saadati R., Yun S., Functional inequalities in fuzzy normed spaces, J. Comput. Anal. Appl., 2017, 22, 601-612Google Scholar

  • [28] Piri H., Rahrovi S., Kumam P., Generalization of Khan fixed point theorem, J. Math. Computer Sci., 2017, 17, 76-83CrossrefGoogle Scholar

  • [29] Rassias Th. M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 1978, 72, 297-300Google Scholar

  • [30] Saadati R., Rassias T. M., Cho Y. J., Approximate (α, β, γ)-derivation on random Lie C*-algebras, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 2015, 109, 1-10Google Scholar

  • [31] Shoaib A., Azam A., Arshad M., Ameer E., Fixed point results for multivalued mappings on a sequence in a closed ball with applications, J. Math. Computer Sci., 2017, 17, 308-316Web of ScienceCrossrefGoogle Scholar

  • [32] Singh D., Chauhan V., Kumam P., Joshi V., Thounthong P., Applications of fixed point results for cyclic Boyd-Wong type generalized F-Psi-contractions to dynamic programming, J. Math. Computer Sci., 2017, 17, 200-215Web of ScienceCrossrefGoogle Scholar

  • [33] Ulam S. M., Problems in modern mathematics, Science Editions John Wiley & Sons, Inc., New York, 1964Google Scholar

  • [34] Wang Z., Sahoo P. K., Approximation of the mixed additive and cubic functional equation in paranormed spaces, J. Nonlinear Sci. Appl., 2017, 10, 2633-2641Web of ScienceGoogle Scholar

  • [35] Zhou M., Liu X. L., Cho Y. J., Damjanovic B., Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problems for some contractive mappings in Ms-metric spaces, J. Nonlinear Sci. Appl., 2017, 10, 2296-2308Web of ScienceGoogle Scholar

  • [36] Cǎdariu L., Radu V., On the stability of the Cauchy functional equation: A fixed point approach, Grazer Math. Ber., 2004, 346, 43-52Google Scholar

About the article

Received: 2017-11-27

Accepted: 2018-02-09

Published Online: 2018-04-13


Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 37–44, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0003.

Export Citation

© 2018 Reza Saadati and Zhihua Wang. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Reza Saadati and Choonkil Park
Advances in Difference Equations, 2018, Volume 2018, Number 1

Comments (0)

Please log in or register to comment.
Log in