The authors consider the equation
where is a linear functional, is continuous and satisfies , , . is defined by , , . Assume , for and some and with respect to a particular exponential ordering. Assume also , where identically 1. It is shown that then the zero solution is exponentially stable. The paper is related to [I. Györi, Differ. Integral Equ. 3, No. 1, 181–200 (1990; Zbl 0726.34054)].