Research articles
ScienceAsia 49 (2023):ID 838-845 |doi:
10.2306/scienceasia1513-1874.2023.052
A complementary Hyers-Ulam stability of alternative equation
of Jensen type
Teerapol Sukhonwimolmal
ABSTRACT: We studied the stability of the alternative functional equation
?f (x ? y) ? 2f (x) + f (x + y)? ? f (x ? y) + f (x + y)? = 0 (*)
for all x, y ? G, where f : G ? B is a function from commutative group G to a real Banach space B, and found that if
?f (x ? y) ? 2f (x) + f (x + y)? ? ? or ?f (x ? y) + f (x + y)? ? ?
for each x, y ? G, then there exists a solution f
?
: G ? B of (*) such that ?f (x) ? f
?
(x)? ? 12?. The general solution
of (*) was also achieved.
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Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002 Thailand |
* Corresponding author, E-mail: teerasu@kku.ac.th
Received 19 Oct 2022, Accepted 4 Jun 2023
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