Double exponential analysis

The subject of this thesis is non-Newtonian analysis produced by the double exponential function. In the thesis, non-Newtonian analyzes first put forward by Michael Grossman and Robert Katz between 1967 and 1970 and the basic definitions and theorems of geometric analysis, one of these analyses, are given. Subsequently, non-Newtonian analysis, which is the generator of the double exponential function α(t) = exp{k⋅exp(t)}, was introduced as an alternative to classical analysis and geometric analysis to work with double exponential functions. This analysis is called double exponential analysis. In the thesis, basic operations in double exponential analysis, double exponential derivative and double exponential integral are given. Finally, the equivalents of the basic definitions and theorems in this analysis.in regard to those of derivatives and integrals in classical analysis were examined.