Strictly nonexpansive, strictly monotone quasi graph-additive functions

Abstract

In this paper, we provide a negative answer to an open problem concerning the functional equation \[f(f(-x)+x)=f(-f(x))+f(x),\] namely by showing that the family of continuous solutions is too rich to admit a complete description. Instead, we characterize the solutions within a certain subfamily.

This manuscript is the revised and corrected version of the previously uploaded manuscript entitled ''Quasi graph-additive functions with a prescribed branch''