Bounds for the Operator Norm on Weighted Cesaro Fractional Difference Sequence Spaces

Abstract

In this paper, we determine the upper and lower bounds for the norm of lower triangular matrix operators on Ces\`{a}ro weighted $(p,v)-$fractional difference sequence spaces of modulus functions. We consider the matrix operators acting between $\ell_{p}(w)$ and $C_{p}(v,\omega,\\\Delta^{(\eta,\ell)},\mathcal{F})$ and identify their bounds and vice-versa. We also investigate the same characteristics for N\"{o}rlund and weighted mean matrix operators.

Keywords

• cesaro sequence space
• $\left(\eta
• \ell\right)-$fractional difference operator
• modulus function
• lower triangular matrix