Application of Geometric Calculus in Numerical Analysis and Difference Sequence Spaces

TL;DR

This paper introduces a new geometric difference sequence space, proves its Banach space properties, explores its duals, and derives geometric Newton-Gregory interpolation formulas.

Contribution

It presents the first geometric difference sequence space and establishes its fundamental properties and duals, along with new interpolation formulas.

Findings

l_infinity^G(Δ_G) is a Banach space.

Computed the α-, β-, and γ-duals of the space.

Derived geometric Newton-Gregory interpolation formulas.

Abstract

The main purpose of this paper is to introduce the geometric difference sequence space $l_\infty^{G} (\Delta_G)$ and prove that $l_\infty^{G} ({\Delta}_{G})$ is a Banach space with respect to the norm $\left\|.\right\|^G_{{\Delta}_G}.$ Also we compute the $\alpha$-dual, $\beta$-dual and $\gamma$-dual spaces. Finally we obtain the Geometric Newton-Gregory interpolation formulae.