The Butzer-Kozakiewicz article on Riemann derivatives of 1954 and its influence

Abstract

The article on Riemann derivatives by P. L. Butzer and W. Kozakiewicz of 1954 was the basis to generalizations of the classical scalar-valued derivatives to Taylor, Peano, and Riemann derivatives in the setting of semigroup theory. The present paper gives an overview of the 1954 article, describes its influence, and integrates it into the literature on related problems. It also describes the state of the mathematics department at McGill University where the article was written.