Strong Converse Inequalities and Qantitative Voronovskaya-Type Theorems for Trigonometric Fej\'er Sums
Strong Converse Inequalities and Qantitative Voronovskaya-Type Theorems for Trigonometric Fej\'er Sums
Let $\sigma_n$ denotes the classical Fej\'er operator for trigonometric expansions. For a fixed even integer $r$, we characterize the rate of convergence of the iterative operators $(I-\sigma_n)^r(f)$ in terms of the modulus of continuity of order $r$ (with specific constants) in all $\mathbb{L}^p$ spaces $1\leq p \leq \infty$. In particular, the constants depend not on $p$. Moreover, we present a quantitative version of the Voronovskaya-type theorems for the operators $(I-\sigma_n)^r(f)$.
Keywords:
Fej\'er operators, iterative combinations rate of convergence, direct and converse results,
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- ISSN: 2651-2939
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2018
- Yayıncı: Tuncer ACAR
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