Volume 20 • Issue 4 • PP: 46-57 • 2023
Hyers - Ulam - Rassias Stability of Various Functional Equations in Non-Archimedean Neutrosophic Normed Spaces
Open Access & Copyright
© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF Abstract
In this paper, we introduce the notion of non- Archimedean neutrosophic normed space and also establish Hyers-Ulam-Rassias-type stability results concerning the Cauchy, Pexiderized Cauchy. We determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framework of non-Archimedean Neutrosophic Normed Space. This work indeed presents a relationship between four various disciplines, the theory of neutrosophic normed space, non – Archimedean, Hyers-Ulam-Rassias stability and functional equation.
Keywords
References
[1] A. Alotaibi and S. A. Mohiuddine, On the stability of a cubic functional equation in random 2-normed spaces, Advances in Difference Equations, vol. 2012, article 39, 2012.
[2] K. Atanassov Intuitionistic fuzzy sets, Fuzzy Sets Syst 20:87-96 (1986).
[3] Z. Gajda, On stability of additive mappings, International Journal of Mathematics and Mathematical Sciences, vol. 14, no. 3, pp. 431–434, 1991.
[4] D. H. Hyers, G. Isac, and T. M. Rassias, Stability of Functional Equations in Several Variables, vol. 34 of Progress in Nonlinear Differential Equations and Their Applications, Birkh¨auser, Boston, Mass, USA, 1998.
[5] M. Jeyaraman, A N. Mangayarkkarasi, V Jeyanthi, R.Pandiselvi. Hyers-Ulam-Rassias stability for functional equation in Neutrosophic Normed Spaces, International Journal of Neutrosophic Science, Vol.18, No.1,127-143, 2022.
[6] M. Jeyaraman, A. Ramachandran and V. B. Shakila, Approximate fixed point Theorems for weak contractions on Neutrosophic Normed space, Journal of computational Mathematics, 6(1), 134-158, 2022.
[7] S.-M. Jung, Hyers-Ulam-Rassias stability of Jensen’s equation and its application, Proceedings of the American Mathematical Society, vol. 126, no. 11, pp. 3137–3143, 1998.
[8] Z. Kominek, On a local stability of the Jensen functional equation, Demonstratio Mathematica, vol. 22, no. 2, pp. 499–507, 1989.
[9] S. A. Mohiuddine and A. Alotaibi, Fuzzy stability of a cubic functional equation via fixed point technique, Advances in Difference Equations, vol. 2012, article 48, 2012.
[10] S. A. Mohiuddine and H. ˇSevli, Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space, Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2137– 2146, 2011.
[11] S. A. Mohiuddine, Stability of Jensen functional equation in intuitionistic fuzzy normed space, Chaos, Solitons & Fractals, vol. 42, no. 5, 2989–2996, 2009.
[12] S. A. Mohiuddine and M. Aiyub, Lacunary statistical convergence in random 2-normed spaces, Applied Mathematics & Information Sciences, vol. 6, no. 3, pp. 581–585, 2012.
[13] M. Mursaleen and S. A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 142–149, 2009.
[14] M. Mursaleen, V. Karakaya, and S. A. Mohiuddine, Schauder basis, separability, and approximation property in intuitionistic fuzzy normed space, Abstract and Applied Analysis, vol. 2010, Article ID 131868, 14 pages, 2010.
[15] M. Mursaleen, On statistical convergence in random 2-normed spaces, Acta Universitatis Szegediensis, vol. 76, no. 1-2, pp. 101–109, 2010.
[16] J. C. Parnami and H. L. Vasudeva, On Jensen’s functional equation, Aequationes Mathematicae, vol. 43, no. 2-3, pp. 211–218, 1992.
[17] T. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Applicandae Mathematicae, vol. 62, no. 1, pp. 23–130, 2000.
[18] R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons and Fractals, vol. 27, no. 2, pp. 331–344, 2006.
[19] F.Smarandache, Neutrosophic set, A generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math., 24, 287-297, 2005.
[20] F.Smarandache, Neutrosophy, Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 1998.
[21] N. Simsek, M. Kirisci, Fixed point theorems in Neutrosophic Metric Spaces, Sigma J. Eng. Nat. Sci., 10(2), 221-230, 2019.
[22] S. M. Ulam, A Collection of Mathematical Problems, vol. 8 of Interscience Tracts in Pure and Applied Mathematics, Interscience Publishers, New York, NY, USA, 1960.
[23] Z. Wang and T.M. Rassias, Intuitionistic fuzzy stability of functional equations associated with inner product spaces, Abstract and Applied Analysis, vol. 2011, Article ID 456182, 19 pages, 2011.
[24] L.A. Zadeh , Fuzzy sets, Inf Control, 8, 338-353, (1965).
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.