Volume 20 , Issue 4 , PP: 46-57, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
R. Muthuraj 1 * , K. Nachammal 2 , M. Jeyaraman 3
Doi: https://doi.org/10.54216/IJNS.200403
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.
Non-Archimedean , Pexiderized Cauchy , Functional Equation , Pexiderized Jensen Functional Equation , Neutrosophic Normed Space.
[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).
