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

Abstract

In this paper, we study the hyperstability problem for the well-known σ-Jensen’s functional equation fxy+fxσy=2fx for all x,y∈S, where S is a semigroup and σ is an involution of S. We present sufficient conditions on E⊂ℝ+S2 so that the inhomogeneous form of σ-Jensen’s functional equation fxy+fxσy=2fx+φx,y for all x,y∈S, where the inhomogeneity φ is given, can be E-hyperstable on S.