Hyperstability of an alternative equation of Jensen type

Teerapol Sukhonwimolmal

ABSTRACT: We studied the stability and hyperstability of the alternative functional equation kf (x ? y) ? 2f (x) + f (x + y)k k f (x ? y) ? ?f (x) + f (x + y)) k = 0 for all x, y ? G using an algebraic approach. The functions are defined as f : G ? B where G is a commutative group and B is a Banach space with ? /? {?2,?1, 0, 2}. We have obtained some necessary conditions on which sufficient conditions for hyperstability were established.

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^a	Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002 Thailand

* Corresponding author, E-mail: teerasu@kku.ac.th

Received 6 Jul 2021, Accepted 7 Nov 2021