The Journal of the Indian Mathematical Society

Lal, Shyam

• Best Approximation of Functions of Zygmund Class by Matrix-euler (Δ·E₁) Means of Fourier Series

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Authors

Shyam Lal ¹, Shireen ¹

Affiliations
1 Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi-221005, IN

Source

The Journal of the Indian Mathematical Society, Vol 82, No 1-2 (2015), Pagination: 61-78

Abstract

In this paper, best approximation of a function f belonging to Zygmund class, Z_α, (0 < α ≤ 1) by Matrix-Euler (Δ·E₁) means of its Fourier Series has been determined.

Keywords

Best Approximation, Fourier Series, E₁ Means, Matrix Summability Means and (Δ·E₁) Summability Means, Zygmund Class.

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• The Method of Summation (E, 1)(N, p_n) and Trigonometric Approximation of Functions in Generalized Holder Metric

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Authors

Shyam Lal ¹, Abhishek Mishra ¹

Affiliations
1 Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi-221005, IN

Source

The Journal of the Indian Mathematical Society, Vol 80, No 1-2 (2013), Pagination: 87-98

Abstract

In this paper, a new estimate for the degree of trigonometric approximation of the function f ∈ H^ω_r class by (E, 1)(N, p_n) summability means of the Fourier Series has been determined.

Keywords

Trigonometric Approximation, Fourier Series, Generalized Minkowski's Inequality, Generalized Holder Metric, (E, 1) Means, (N, p_n) Means and (E, 1)(N, p_n) Summability Means.

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• On the Approximation of Function f(x,y) Belonging to Lipschitz Class by Matrix Summability Method of Double Fourier Series

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Authors

Shyam Lal ¹

Affiliations
1 Department of Mathematics, Banaras Hindu University, Varanasi-221005, IN

Source

The Journal of the Indian Mathematical Society, Vol 78, No 1-4 (2011), Pagination: 93-101

Abstract

In this paper, a new estimate for the degree of approximation of a function f(x,y) belonging to Lip(α,β) class by double matrix summability method of its double Fourier series has been determined.

Keywords

Degree of Approximation, Double Fourier Series, Double Matrix Summability Means, Functions of Lip(α,β) Class, (c,1,1), (H,1,1) and (N, p_m, q_n) Means.

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