Row-summable matrices with application to generalization of Schröder’s and Abel’s functional equations

In this paper, the author discusses a generalization of Schröder’s and Abel’s functional equation of the form ∑ n α n ( x ) f ( u n ( x ) ) = g ( x ) . In fact, using the theory of operators and infinite matrices, we show under certain conditions this equation has only a unique bounded solution f : X → R .