On Approximation of Functions Belonging to Lip (α,r) Class and to Weighted W (Lr, ξ(t)) class by Product Means
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A good amount of work has been done on degree of approximation of functions belonging to Lipα, Lip (α, r) ; Lip (ξ(t), r) and W (Lr, ξ(t)) classes using Cesaro, Norlund and generalised Norlund single summability methods by a number of researchers ([1], [10],[8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N; pn)(C; 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function f ∈ Lip (α, r) class and f ∈ W (Lr, ξ(t)) class by (N, pn)(C, 1)product summability means of its Fourier series.
Abstract
A good amount of work has been done on degree of approximation of functions belonging to Lipα, Lip (α, r) ; Lip (ξ(t), r) and W (Lr, ξ(t)) classes using Cesaro, Norlund and generalised Norlund single summability methods by a number of researchers ([1], [10],[8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N; pn)(C; 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function f ∈ Lip (α, r) class and f ∈ W (Lr, ξ(t)) class by (N, pn)(C, 1)product summability means of its Fourier series.
참고문헌 (12)
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