In this article we introduce the paranormed sequence spaces ( f ,Λ,∆m, p), c0( f ,Λ,∆m, p) and l∞( f ,Λ,∆m, p), associated with the multiplier sequence Λ = (λk), defined by a modulus function f . We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results.

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for ...

The idea of difference sequence spaces were introduced by Kizmaz [6] and generalized by Et. and Colak [4]. Later Tripathy, Esi and Tripathy [15] introduced the notion of the new difference operator ∆m for n,m ∈ N . In this paper we introduced some new type of generalized difference sequence spaces defined by a modulus function and the new type of statistically convergent generalized difference ...