Generalized derivates and derivatives of typical continuous functions
We present here briefly some results on the nature of various known generalized derivates, and some generalized new derivatives, of typical continuous functions. Any property is said to hold for typical continuous functions if it holds for a residual set of functions in the Banach space \(C\) of continuous real valued functions on the interval \(I \equiv [0,1]\) under the uniform norm. These results will be presented in greater detail in the author's paper [``Generalized derivates and derivatives of typical continuous functions'' (to appear in Real Anal. Exch.)], and would appear subsequently with proofs in his forthcoming monograph [``A unified theory of differentiation via some new derivatives''].
scientific article; zbMATH DE number 1134757