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 to extend the determination of 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.
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