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. - 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. 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. - 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. 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. - Department of Mathematics Education, Gyeongsang Natoinal University, Jinju 660-701, Korea. Phatiphat Thounthong - 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. 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. - 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.
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.
Kittipong Wongkum, Poom Kumam, Yeol Je Cho, Phatiphat Thounthong, Parin Chaipunya, On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1399--1406
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. J. Nonlinear Sci. Appl. (2017); 10(4):1399--1406
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 Applications, 10, no. 4 (2017): 1399--1406
