On stability of the functional equation of p-Wright affine functions in (2, α)-Banach spaces

Abstract

Abstract Stability of functional equations has recent applications in many fields. We show that the stability results obtained by J. Brzdęk and concerning the functional equation of the p-Wright affine function: f(p x 1+(1−p)x 2)+f((1−p)x 1+p x 2)=f(x 1)+f(x 2), can be proved also in (2, α)-Banach spaces, for some real number α∈(0,1). This is done using some fixed-point theorem.

Keywords

• Hyers-Ulam stability
• p-Wright convexity
• Affine function
• Banach spaces