Korovkin Approximation Theorem with Ω Striped

Malik Saad Al-Muhja,Zurni B Omar,Masnita Misiran,Sui Yang Khoo,Mohammad Mursaleen

doi:10.5539/jmr.v10n1p20

Malik Saad Al-Muhja, Zurni B Omar + Show 3 more

Open Access

https://doi.org/10.5539/jmr.v10n1p20

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Abstract

In this paper, we discuss some theorem reached M. Mursaleen, there are several properties of statistical lacunary summability presented (Mursaleen, M. & Alotaibi,A., 2011; Mursaleen, M. &Alotaibi, A., 2011; Edely, O. H. & Mursaleen, M., 2009). This is concerned the motivate to narrowly delineated context denoted by Ω striped usage in prove our theorem (theorem A). We introduce some piecewise polynomial functions (Kopotun,K. A., 2006) and some results Korovkin theorem.

Highlights

Introduction and Main ResultsThe aim of this paper a completed the striped used in many area of Korovkin theorem (Mursaleen, M. & Alotaibi, A., 2011; Al-Muhja, M., 2015).We will need accept the following: LetK ⊆ N
We introduce some piecewise polynomial functions
Definition 1.8 (Al-Muhja, M., 2015) A linear differential operator Υ on Gs is said to be homogeneous of degree λ if Υ(s ∘ γτ) = τλ(Υs) ∘ γτ, for any s ∈ Gs and τ > 0

Summary

Introduction

Introduction and Main ResultsThe aim of this paper a completed the striped used in many area of Korovkin theorem (Mursaleen, M. & Alotaibi, A., 2011; Al-Muhja, M., 2015).We will need accept the following: LetK ⊆ N. A. & Orhan, C., 1993) A sequence x = (xk) is said to be lacunary statistically convergent to L, if for every ε > 0, the set Kε ≔ {k ∈ N: |xk − L| ≥ ε} has θ–density zero, i.e. δθ(Kε) = 0. In this case we write Sθ − limi xi = L, and we denote the set of all lacunary statistically convergent sequence by Sθ.

Results

Conclusion