A differentiable function at a point in Banach spaces is defined in terms of the existence of a linear approximation of the function at that point. The discussion highlights the ambiguity in definitions found in common resources like Wikipedia, suggesting that while they may be equivalent, they do not align with specific usage in certain contexts. The user ultimately found a definition from a less common source, indicating the need for precise references in advanced mathematical topics.
PREREQUISITESMathematicians, students of functional analysis, and researchers focusing on advanced calculus and Banach space theory.