On Certain Difference Operators and Their Explicitly Inverses

Abstract

In recent years, a number of extensive applications of
difference operators through sequence spaces have been developed.
The most crucial application is being used in the study of
functional analysis, operator theory and matrix theory. In this
context, the present article makes an attempt to provide a survey
on various difference operators and unify them by introducing two
$m+1$-th sequential band matrices. The purpose of this work is
also extended to determine their inverses and derive an adaptive
recursive free formula for matrix inversions. We provide two
relevant formulas for inversion of $m+1$-th sequential lower and
upper band matrices. Subsequently, the idea is being applied to
develop a new explicitly formula for matrix inversion.