Modular convergence in $H$-Orlicz spaces of Banach valued functions

Abstract

In this article we develop the theory of $H$-Orlicz space generated by generalised Young function. Modular convergence of $H$-Orlicz space for the case of vector-valued functions and norm convergence in $\mcH^θ(X, \barμ)$ where $X$ is any Banach space are discussed. Relationships of modular convergence and norm convergence of $H$-Orlicz spaces are discussed.