Bigeometric Ces$\grave{\text{a}}$ro difference sequence spaces and Hermite interpolation

TL;DR

This paper introduces new bigeometric difference sequence spaces, explores their duals and transformations, and develops a Hermite-like interpolation polynomial within bigeometric calculus, expanding the mathematical framework in this area.

Contribution

It presents novel bigeometric difference sequence spaces, characterizes their duals, studies matrix transformations, and constructs a Hermite-type interpolation polynomial in bigeometric calculus.

Findings

Determined the α-duals of the new sequence spaces.

Analyzed matrix transformations for these spaces.

Developed a Hermite interpolation polynomial in bigeometric calculus.

Abstract

In this paper, we introduce some difference sequence spaces in bigeometric calculus. We determine the $\alpha$-duals of these sequence spaces and study their matrix transformations. We also develop an interpolating polynomial in bigeometric calculus which is analogous to the classical Hermite interpolating polynomial.