New random version of stability via fixed point method
DOI:
https://doi.org/10.29304/jqcm.2023.15.1.1144Keywords:
Cubic mapping, stability, random normed space (ȐṄ −space).Abstract
We studied the stability of the cubic functional equation:
3 ß( +3 ƴ)-ß(3 + ƴ)=12 [ß( + ƴ)+ß( - ƴ)]+80 ß(ƴ)-48 ß( ). (1.1)
via fixed point method in random normed space (ȐṄ −space).
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References
[1] Alshybani, SH., Vaezpour, S.M., & Saadati, R. (2017). Generalized Hyers-Ulam stability of mixed type additive-quadratic functional equation in random normed spaces. J. Math. Anal, 8(5), 12-26.
[2] Cadariu, L. I. V. I. U., & Radu, V. (2009). Fixed points and generalized stability for functional equations in abstract spaces. J. Math. Inequal, 3, 463-473.
[3] Cho, Y. J., Rassias, T. M., & Saadati, R. (2013). Stability of functional equations in random normed spaces (Vol. 86). Springer Science & Business Media..
[4]. Jung, C. F. (1969). On generalized complete metric spaces. Bulletin of the American Mathematical Society, 75(1), 113-116..
[5]. Luxemburg, W. A. J. (1958). On the convergence of successive approximations in the theory of ordinary differential equations. Canadian Mathematical Bulletin, 1(1), 9-20.
[6] Radu, V. (2003). The fixed point alternative and the stability of functional equations. Fixed point theory, 4(1), 91-96.
[7] Patel, R. M., Bhardwaj, R., & Choudhary, P. Common Fixed Point Theorem for ψ-weakly commuting maps in L-Fuzzy Metric Spaces for integral type.
[8] Xu, T., Rassias, J., Rassias, M., & Xu, W. (2011). A fixed point approach to the stability of quintic and sextic functional equations in quasi--normed spaces. Journal of Inequalities and Applications, 2010, 1-23.
[9] Xu, T. Z., Rassias, M. J., XU, X., & Rassias, J. M. (2012). A fixed point approach to the intuitionistic fuzzy stability of quintic and sextic functional equations.
[10] Ulam, S. M. (1964). Problems in Modern Mathematics, science editions, Wiley, NewYork, 1964 (Chapter VI, Some Questions in Analysis: 1, Stability).
[11] Benzarouala, C., Brzdęk, J., & Oubbi, L. (2023). A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces. Journal of Fixed Point Theory and Applications, 25(1), 1-38.
[12] Ciepliński, K. (2023). Stability of a General Functional Equation in m-Banach Spaces. Bulletin of the Malaysian Mathematical Sciences Society, 46(2), 1-11.
[2] Cadariu, L. I. V. I. U., & Radu, V. (2009). Fixed points and generalized stability for functional equations in abstract spaces. J. Math. Inequal, 3, 463-473.
[3] Cho, Y. J., Rassias, T. M., & Saadati, R. (2013). Stability of functional equations in random normed spaces (Vol. 86). Springer Science & Business Media..
[4]. Jung, C. F. (1969). On generalized complete metric spaces. Bulletin of the American Mathematical Society, 75(1), 113-116..
[5]. Luxemburg, W. A. J. (1958). On the convergence of successive approximations in the theory of ordinary differential equations. Canadian Mathematical Bulletin, 1(1), 9-20.
[6] Radu, V. (2003). The fixed point alternative and the stability of functional equations. Fixed point theory, 4(1), 91-96.
[7] Patel, R. M., Bhardwaj, R., & Choudhary, P. Common Fixed Point Theorem for ψ-weakly commuting maps in L-Fuzzy Metric Spaces for integral type.
[8] Xu, T., Rassias, J., Rassias, M., & Xu, W. (2011). A fixed point approach to the stability of quintic and sextic functional equations in quasi--normed spaces. Journal of Inequalities and Applications, 2010, 1-23.
[9] Xu, T. Z., Rassias, M. J., XU, X., & Rassias, J. M. (2012). A fixed point approach to the intuitionistic fuzzy stability of quintic and sextic functional equations.
[10] Ulam, S. M. (1964). Problems in Modern Mathematics, science editions, Wiley, NewYork, 1964 (Chapter VI, Some Questions in Analysis: 1, Stability).
[11] Benzarouala, C., Brzdęk, J., & Oubbi, L. (2023). A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces. Journal of Fixed Point Theory and Applications, 25(1), 1-38.
[12] Ciepliński, K. (2023). Stability of a General Functional Equation in m-Banach Spaces. Bulletin of the Malaysian Mathematical Sciences Society, 46(2), 1-11.
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Published
2023-02-17
How to Cite
Shalaal, A. M., & ALshybani, S. (2023). New random version of stability via fixed point method. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(1), Math Page 1–6. https://doi.org/10.29304/jqcm.2023.15.1.1144
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Computer Articles
