Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces

Abstract

Abstract In this article, with simple and short proofs without applying fixed point theorems, some hyperstability results corresponding to the functional equations of Cauchy and Jensen are presented in 2-normed spaces. We also obtain some results on hyperstability for the general linear functional equation f ( a x + b y ) = A f ( x ) + B f ( y ) + C $f(ax+by)=Af(x)+Bf(y)+C$ .

Keywords

• 2-normed space
• Cauchy functional equation
• Jensen functional equation
• General linear functional equation
• Hyperstability