Some Characteristics of Matrix Operators on Generalized Fibonacci Weighted Difference Sequence Space

Abstract

The forthcoming property of this manuscript is its calculating of the goal of norms and lower bounds of matrix operators taken from the weighted sequence space ℓp(w) onto a novel one defined in the present article as the generalized Fibonacci weighted difference sequence space. In this process, first of all the Fibonacci difference matrix F˜(r,s) and the space composed of sequences of which F˜(r,s)-transforms lie in ℓp(w˜), where r,s∈R are defined. Additionaly, since the seminormed space ℓp(w˜,F˜(r,s)) has the absolute homogeneous property, the topological characteristics on it are distributed symmetrically everywhere in the space.

Keywords

• Fibonacci numbers
• sequence spaces
• matrix operators
• quasi-summable matrices