Geodesic
On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces
Wongkum, Kittipong1 ; Kumam, Poom2 ; Cho, Yeol Je3 ; Thounthong, Phatiphat4 ; Chaipunya, Parin1
1 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;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
2 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;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;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
3 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;Department of Mathematics Education, Gyeongsang Natoinal University, Jinju 660-701, Korea
4 Renewable Energy Research Centre, King Mongkuts University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand;Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkuts University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 4, p. 1399-1406.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.04.10
Classification : 39B82, 47H10
Keywords: Quartic mapping, generalized UHR stability, modular space.

Wongkum, Kittipong 1 ; Kumam, Poom 2 ; Cho, Yeol Je 3 ; Thounthong, Phatiphat 4 ; Chaipunya, Parin 1

1 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;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
2 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;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;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
3 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;Department of Mathematics Education, Gyeongsang Natoinal University, Jinju 660-701, Korea
4 Renewable Energy Research Centre, King Mongkuts University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand;Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkuts University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand 
@article{JNSA_2017_10_4_a9,
     author = {Wongkum, Kittipong and Kumam, Poom and Cho, Yeol Je and Thounthong, Phatiphat and Chaipunya, Parin},
     title = {On the generalized {Ulam-Hyers-Rassias} stability for quartic functional equation in modular spaces},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {1399-1406},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2017},
     doi = {10.22436/jnsa.010.04.10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.04.10/}
}
TY  - JOUR
AU  - Wongkum, Kittipong
AU  - Kumam, Poom
AU  - Cho, Yeol Je
AU  - Thounthong, Phatiphat
AU  - Chaipunya, Parin
TI  - On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces
JO  - Journal of nonlinear sciences and its applications
PY  - 2017
SP  - 1399
EP  - 1406
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.04.10/
DO  - 10.22436/jnsa.010.04.10
LA  - en
ID  - JNSA_2017_10_4_a9
ER  - 
%0 Journal Article
%A Wongkum, Kittipong
%A Kumam, Poom
%A Cho, Yeol Je
%A Thounthong, Phatiphat
%A Chaipunya, Parin
%T On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces
%J Journal of nonlinear sciences and its applications
%D 2017
%P 1399-1406
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.04.10/
%R 10.22436/jnsa.010.04.10
%G en
%F JNSA_2017_10_4_a9
Wongkum, Kittipong; Kumam, Poom; Cho, Yeol Je; Thounthong, Phatiphat; Chaipunya, Parin. On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 4, p. 1399-1406. doi : 10.22436/jnsa.010.04.10. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.04.10/

[1] Aoki, T. On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, Volume 2 (1950), pp. 64-66 | DOI

[2] Cho, Y. J.; Park, C.-K.; Rassias, T. M.; Saadati, R. Stability of functional equations in Banach algebras, Springer, Cham, 2015 | DOI

[3] Cho, Y. J.; Rassias, T. M.; Saadati, R. Stability of functional equations in random normed spaces, Springer Optimization and Its Applications, Springer, New York, 2013

[4] Hyers, D. H. On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., Volume 27 (1941), pp. 222-224 | DOI

[5] Khamsi, M. A. Quasicontraction mappings in modular spaces without \(\Delta_2\)-condition, Fixed Point Theory Appl., Volume 2008 (2008), pp. 1-6 | DOI | Zbl

[6] Lee, Y.-S.; Chung, S.-Y. Stability of quartic functional equations in the spaces of generalized functions, Adv. Difference Equ., Volume 2009 (2009), pp. 1-16

[7] Lee, S. H.; Im, S. M.; Hwang, I. S. Quartic functional equations, J. Math. Anal. Appl., Volume 307 (2005), pp. 387-394

[8] Rassias, T. M. On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., Volume 72 (1978), pp. 297-300 | DOI

[9] Rassias, J. M. Solution of the Ulam stability problem for quartic mappings, Glas. Mat. Ser. III, Volume 34(54) (1999), pp. 243-252

[10] Ulam, S. M. Problems in modern mathematics, Science Editions John Wiley & Sons, Inc., New York, 1964

Cité par Sources :