On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces

Authors

Kittipong Wongkum - KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
Poom Kumam - KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
Yeol Je Cho - KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
Phatiphat Thounthong - Renewable Energy Research Centre, King Mongkuts University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand.
Parin Chaipunya - KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.

Abstract

In this paper, we prove the generalized UHR stability of a quartic functional equations f(2x + y) + f(2x - y) = 4f(x + y) + 4f(x - y) + 24f(x) - 6f(y) via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces by the modular which is l.s.c. and convex.

Keywords

Quartic mapping, generalized UHR stability, modular space.

References

[1] T. Aoki,/ On the stability of the linear transformation in Banach spaces,/ J. Math. Soc. Japan,/ 2 (1950), 64–66.
[2] Y. J. Cho, C.-K. Park, T. M. Rassias, R. Saadati,/ Stability of functional equations in Banach algebras,/ Springer, Cham,/ (2015).
[3] Y. J. Cho, T. M. Rassias, R. Saadati,/ Stability of functional equations in random normed spaces,/ Springer Optimization and Its Applications, Springer, New York,/ (2013).
[4] D. H. Hyers,/ On the stability of the linear functional equation,/ Proc. Nat. Acad. Sci. U. S. A.,/ 27 (1941), 222–224.
[5] M. A. Khamsi,/ Quasicontraction mappings in modular spaces without \(\Delta_2\)-condition,/ Fixed Point Theory Appl.,/ 2008 (2008), 6 pages.
[6] Y.-S. Lee, S.-Y. Chung,/ Stability of quartic functional equations in the spaces of generalized functions,/ Adv. Difference Equ.,/ 2009 (2009), 16 pages.
[7] S. H. Lee, S. M. Im, I. S. Hwang,/ Quartic functional equations,/ J. Math. Anal. Appl.,/ 307 (2005), 387–394.
[8] T. M. Rassias,/ On the stability of the linear mapping in Banach spaces,/ Proc. Amer. Math. Soc.,/ 72 (1978), 297–300.
[9] J. M. Rassias,/ Solution of the Ulam stability problem for quartic mappings,/ Glas. Mat. Ser. III,/ 34(54) (1999), 243–252.
[10] S. M. Ulam,/ Problems in modern mathematics,/ Science Editions John Wiley & Sons, Inc., New York,/ (1964).

Downloads

XML export