On an equation characterizing multi-Jensen-quartic mappings and its stability. (English) Zbl 1469.39013
J. M. Rassias [Glas. Mat., III. Ser. 34, No. 2, 243–252 (1999; Zbl 0951.39008)] introduced the following quartic functional equation: \[Q(x+2y)+Q(x-2y)= 4Q(x+y)+4Q(x-y)-6Q(x)+24Q(y).\] Motivated by the above equation, the authors define some multi-quartic mappings and characterize them in terms of a suitable functional equation. They also introduce the multi-Jensen-quartic mappings which are Jensen in each of some \(k\) variables and are quartic in each of the other variables. In addition, they present a characterization of such mappings. They prove the generalized Hyers-Ulam stability for multi-Jensen-quartic functional equations by using the fixed point method.
Reviewer: Maryam Amyari (Mashhad)
MSC:
| 39B52 | Functional equations for functions with more general domains and/or ranges |
| 39B72 | Systems of functional equations and inequalities |
| 39B82 | Stability, separation, extension, and related topics for functional equations |
Keywords:
Banach space; multi-Jensen mapping; multi-Jensen-quartic mapping; multi-quartic mapping; Hyers-Ulam stability; hyperstabilityCitations:
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