Differentiation in Banach Spaces (original) (raw)

This paper explores the concept of differentiation in the context of Banach spaces, focusing on the definition and properties of derivatives applicable to functions defined on such spaces. The content is structured into two main chapters: the first detailing basic definitions and properties of these derivatives, and the second discussing various applications of the theory. It is essential for the reader to have a foundational understanding of limits, inequalities, and the properties of linear transformations.