Existence and uniqueness of solutions of Hahn difference equations

Abstract

Hahn introduced the difference operator D q, f (t) = (f (qt + ) -f (t))/(t(q -1) + ) in 1949, where 0 < q < 1 and > 0 are fixed real numbers. This operator extends the classical difference operator f (t) = (f (t + ) -f (t))/ as the Jackson q-difference operator D q f (t) = (f (qt) -f (t))/(t(q -1)).