Some basic properties of G-Calculus and its applications in numerical analysis

Objective of this paper is to introduce a new type of calculus which will be called G-Calculus based on non-Newtonian calculus introduced by Grossman and Katz \cite{GrossmanKatz}. The basic difference between geometric calculus defined by Grossman and Katz and the present G-calculus is that Grossman took the values of the argument as $x,x+h,x+2h,\mathrm{.}\mathrm{.}\mathrm{.}$ but here in G-calculus we take the values as $x,x\oplus h,x\oplus e^2\odot h,x\oplus e^3\odot h\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}$ This calculus will have great deal with numerical analysis which are discussed in the last section of this paper.