Volume 18 • Issue 1 • PP: 127-143 • 2022
Hyers-Ulam-Rassias Stability for Functional Equation in Neutrosophic Normed Spaces
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In Neutrosophic Normed spaces, we investigate a unique quadratic function and a unique additive quadratic function of the Hyers-Ulam-Rassias stability for the functional equation 
which is said to be a functional equation associated with inner products
space.
Keywords
References
[1] T. M. Rassias, “New characterizations of inner product spaces,” Bulletin des Sciences Mathematiques, vol. 108, no. 1, pp. 95-99, 1984.
[2] C. Park, J. S. Huh, W. J. Min, D. H. Nam, and S. H. Roh, “Functional equations associated with inner product spaces,” The Journal of Chungcheong Mathematical Society, vol. 21, pp. 455-466, 2008.
[3] C. Park, W. G. Park, and A. Najati, “Functional equations related to inner product spaces,” Abstract and Applied Analysis, vol. 2009, Article ID 907121, 11 pages, 2009.
[4] A. Najati and T. M. Rassias, “Stability of a mixed functional equation in several variables on Banach modules,” Nonlinear Analysis. Theory, Methods & Applications., vol. 72, no. 3-4, pp. 1755-1767, 2010.
[5] C. Park, “Fuzzy stability of a functional equation associated with inner product spaces,” Fuzzy Sets and Systems, vol. 160, no. 11, pp. 1632-1642, 2009.
[6] S. M. Ulam, Problems in Modern Mathematics, John Wiley & Sons, New York, NY, USA, 1964.
[7] D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, pp. 222-224, 1941.
[8] T. Aoki, “On the stability of the linear transformation in Banach spaces,” Journal of the Mathematical Society of Japan, vol. 2, pp. 64-66, 1950.
[9] T. M. Rassias, “On the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, no. 2, pp. 297-300, 1978.
[10] R. P. Agarwal, B. Xu, and W. Zhang, “Stability of functional equations in single variable,” Journal of Mathematical Analysis and Applications, vol. 288, no. 2, pp. 852-869, 2003.
[11] G. L. Forti, “Hyers-Ulam stability of functional equations in several variables,” Aequationes Mathematicae, vol. 50, no. 1-2, pp. 143-190, 1995.
[12] P. Gavrut ¸a, “A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings,” Journal of Mathematical Analysis and Applications, vol. 184, no. 3, pp. 431-436, 1994.
[13] D. H. Hyers, G. Isac, and T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, Switzerland, 1998.¨
[14] S. M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, Fla, USA, 2001.
[15] S. M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, vol. 48, Springer, New York, NY, USA, 2011.
[16] P. Kannappan, Functional Equations and Inequalities with Applications, Springer, New York, NY, USA, 2009.
[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] T. M. Rassia, Functional Equations, Inequalities and Applications, Kluwer Academic, Dordrecht, The Netherlands, 2003.
[19] A. K. Mirmostafaee, M. Mirzavaziri, and M. S. Moslehian, “Fuzzy stability of the Jensen functional equation,” Fuzzy Sets and Systems, vol. 159, no. 6, pp. 730-738, 2008.
[20] A. K. Mirmostafaee and M. S. Moslehian, “Fuzzy versions of Hyers-Ulam-Rassias theorem,” Fuzzy Sets and Systems, vol. 159, no. 6, pp. 720-729, 2008.
[21] A. K. Mirmostafaee and M. S. Moslehian, “Fuzzy almost quadratic functions,” Results in Mathematics, vol. 52, no. 1-2, pp. 161-177, 2008.
[22] A. K. Mirmostafaee and M. S. Moslehian, “Fuzzy approximately cubic mappings,” Information Sciences, vol. 178, no. 19, pp. 3791-3798, 2008.
[23] B. Schweizer and A. Sklar, “Statistical metric spaces,” Pacific Journal of Mathematics, vol. 10, pp. 313334, 1960.
[24] F. Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning. Ann Arbor, Mi.chigan, USA. (1998).
[25] F. Smarandache, A unifying field in logics: Neutrosophic logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, Phoenix: Xiquan. (2003).
[26] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets. International Journal of Pure and Applied Mathematics 24(2005), 287 - 297.
[27] F. Smarandache, Introduction to neutrosophic measure, neutrosophic integral, and neutrosophic probability, sitech & educational. Columbus: Craiova, (2013).
[28] L. A.Zadeh, Fuzzy Sets, Inform. And Control, 1965, Vol. 8, 338-353.
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