We present Kuelbs-Steadman spaces designed for vector-valued functions that take values in Banach spaces. Our study focuses on their fundamental properties and their embeddings within L^p spaces. Additionally, we introduce a fixed point theorem based on the concept of a measure of noncompactness in KS^p (X). Furthermore, we demonstrate the existence theorem for Cauchy? s problem defined by? ? (? ) =? (? ,? ? ) and the inclusion? ? ? ? (? ,? ? ) in KS^p (X), where? is a Henstock-Kurzweil integrable function.
Hemanta Kalita (Wed,) studied this question.