SCIENCE ASIA

Volume 46, No. 03, Month JUNE, Year 2020, Pages 368 - 375

A general form of an alternative functional equation related to the jensen’s functional equation

Nataphan Kitisin, Choodech Srisawat

Abstract Download PDF

Given integers ,, such that (,, ) 6= (k,􀀀2k, k) for all k 2 Z, we will establish a criterion for the existence of the general solution of the alternative Jensen’s functional equation of the form f (x y􀀀1)􀀀2f (x)+ f (x y) = 0 or f (x y􀀀1)+ f (x)+ f (x y) = 0, where f is a mapping from a group (G,
) to a uniquely divisible abelian group (H,+). We also find the general solution in the case when G is a cyclic group.

Keywords

alternative equation, Jensen’s functional equation, additive function

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