A GENERALIZATION OF THE STABILITY OF A QUARTIC FUNCTIONAL EQUATION IN QUASI-β-NORMED SPACES WITH THE FIXED POINT METHOD
DOI:
https://doi.org/10.5281/9sdkzd34Abstract
The stability of functional equations has been a central topic in
mathematical analysis due to its significance in various fields, including approximation theory, dynamical systems, and optimization problems. In this
paper, by utilizing the fixed point method, we investigate the Hyers-Ulam stability of one form of the quartic functional equation involving an unknown
function from a normed space into a quasi-β-Banach space. This approach not
only provides constructive proof but also demonstrates the versatility of fixed
point theory in solving stability problems. The results obtained in this study
extend existing works on quartic functional equations and offer a more general
framework applicable to quasi-β-Banach spaces.
References
[1] J. K. Chung and P. K. Sahoo, On the general solution of a quartic functional equation, Bull.
Korean Math. Soc. 40 (2003), 565-576.
[2] J. B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a
generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309.
[3] C. Hengkrawit and A. Thanyacharoen, A general solution of a generalized quartic functional
equation and its stability, Int. J. Pure Appl. Math. 85 (2013), 691-706.
[4] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A.
27 (1941), 222-224.
[5] P. G˜avruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive
mappings, J. Math. Anal. Appl. 184 (1994), 431-436.
[6] M. Mirzavaziri and M. S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. 37(3) (2006), 361-376.
[7] J. M. Rassias, Solution of the Ulam stability problem for quartic mappings, Glasnik
Matemati˜cki, 34 (1999), 243-252.
[8] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math.
Soc. 72 (1978), 297-300.
[9] S. Rolewicz, Metric Linear Spaces, PWN-Polish Sci. Publ., Warszawa, Reidel, Dordrecht,
(1984).
[10] S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, (1964).
[11] Y. S. Yun and C. I. Kim, Fixed point approach to stability of additive-quadratic functional
equations in quasi-β-normed spaces, Int. J. Math. Anal. 10 (2016), 429-438
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