On Banach Space Valued Function Space of Bounded Type Defined by Orlicz Function

The present work introduces and investigates a new class of Banach space-valued functions of bounded type, constructed using an Orlicz function. It serves as a natural extension of the classical space of bounded complex sequences commonly studied in functional analysis. In addition, we examine the linear and topological properties of this space under a suitable natural norm. The role of the Δ2-condition in ensuring the equality of associated classes of Banach space-valued functions of bounded type, is highlighted through illustrative examples