Abstract

The main result of this work is a simple characterization of the hyperstability of functional equations in a very general framework: for functions with the codomain endowed with a generalized homogeneous premetric. We also give some particularizations on Abelian groups equipped with generalized homogeneous norms, obtaining, among others, improvements of similar known results for Cauchy-type, Jensen-type equations, but also for equations having compound functions as solutions.

Keywords: Equation on restricted domain; hyperstability; Cauchy-type equation; Jensen-type equation.

MSC: 39B82, 39B52, 39A70, 39B62, 39A10

DOI: 10.57016/MV-ZICO1528

Pages:  1--7