Weighted averages and their comparison in non-Newtonian analysis

The years between 1600-1700 were a period of significant developments in mathematics. One of the most important developments of this period was the independent discovery of derivatives and integrals by Newton (1643-1727) and Leibniz (1646-1716). As a result, the concept of "Integral Calculus" gained importance. It paved the way for these developments and ensured their progress. In the 1970s, Grosmann and Katz continued a new construction analysis, mainly thanks to one-to-one and surjective generators, as an alternative to the classical analysis established by Newton and Leibniz. This analysis is called ''Non-Newtonian Analysis". In this master's thesis; averages and some of their applications in non-Newtenian analysis were made in detail. In addition, in which cases they are reduced to classical arithmetic and their comparison with each other were examined.