On a Pexider type equation on $Δ^+$

Abstract

The Pexider equation in question is defined with the use of t-norm and is considered in the space $Δ^+$ of all non decreasing functions $F$ from $ℝ^+$ into $I$ that satisfy $F(0) = 0, F(∞) = 1$ and are left-continuous on $(0,∞)$. The general solution of the equation is found as well as, under certain regularity conditions solutions of more explicit from are exhibited.