On the Function Sequences and Series in the Non-Newtonian Calculus

Abstract

The purpose of this study is to examine the function sequences and series in the non-Newtonian real numbers. Firstly, the information about the studies that are done until today and the application areas, was briefly given. Non-Newtonian calculus was introduced which is an alternative to the classical calculus, definitions, theorems and properties were given. *-Function sequence, *-function series, *-pointwise convergence and *-uniform convergence were introduced and theorems were proven which are exposed important differences between *-pointwise convergence and *-uniform convergence. In addition, *-convergence tests such as *-Cauchy criterion and *-Weierstrass M-criterion were obtained. The relationship between *-uniform convergence of the *-continuity, *-integral and *-derivative was examined respectively.