Fixed Points and Quartic Functional Equations in β-Banach Modules

• Published in: Resultate der Mathematik Vol. 62; no. 1-2; pp. 137 - 155
• Main Authors: Gordji, M. Eshaghi, Khodaei, H., Najati, A.
• Format: Journal Article
• Language: English
• Published: Basel SP Birkhäuser Verlag Basel 01.09.2012
• Subjects: Mathematics; Mathematics and Statistics; 39B52; generalized metric space; generalized Hyers–Ulam stability; quartic functional equation; Primary 47H10; Banach module over a Banach algebra; Secondary 39B82; 46H25; Fixed point method
• ISSN: 1422-6383; 1420-9012
• DOI: 10.1007/s00025-011-0135-8

Let M  = { 1, 2, . . . ,  n  } and let , where n is an integer greater than 1. Denote by I c for We investigate the solution of the following generalized quartic functional equation in β -Banach modules on a Banach algebra, where with a ℓ  ≠ ±1 for all and a n  = 1. Moreover, using the fixed point method, we prove the generalized Hyers–Ulam stability of the above generalized quartic functional equation. Finally, we give an example that the generalized Hyers–Ulam stability does not work.