On the E-Hyperstability of the Inhomogeneous σ-Jensen's Functional Equation on Semigroups.

In this paper, we study the hyperstability problem for the well-known σ -Jensen's functional equation f x y + f x σ y = 2 f x for all x , y ∈ S , where S is a semigroup and σ is an involution of S. We present sufficient conditions on E ⊂ ℝ + S 2 so that the inhomogeneous form of σ -Jensen's functional equation f x y + f x σ y = 2 f x + φ x , y for all x , y ∈ S , where the inhomogeneity φ is given, can be E -hyperstable on S. [ABSTRACT FROM AUTHOR]