arXiv subjects
Publications and source records attributed to Khirod Boruah.
Based on M. Grossman in \cite{Grossman83} and Grossman an Katz \cite{GrossmanKatz}, in this paper we discuss about the applications of bigeometric calculus in different branches of mathematics and economics.
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 $x, x+ h, x+2h,...$ but here in G-calculus we take the values as $x, x\oplus h, x\oplus e^2\odot h, x\oplus e^3\odot h....$ This calculus will have great deal with numerical analysis which are discussed in the last section of this paper.
The main purpose of this paper is to introduce the geometric difference sequence space $l_\infty^{G} (Δ_G)$ and prove that $l_\infty^{G} (Δ_{G})$ is a Banach space with respect to the norm $\left\|.\right\|^G_{Δ_G}.$ Also we compute the $α$-dual, $β$-dual and $γ$-dual spaces. Finally we obtain the Geometric Newton-Gregory interpolation formulae.
Objective of this paper is to introduce the generalized geometric difference sequence spaces $l_\infty^{G}(Δ^m_G), c^G(Δ^m_G), c_0^{G}(Δ^m_G)$ and to prove that these are Banach spaces. Then we prove some inclusion properties. Also we compute their dual spaces.