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Wedetermine the degree of approximation of conjugate of a function belonging to Lip(ξ(t),p) class by matrix summability means of a conjugate series of a Fourier series. 2000 Mathematics Subject Classification. 42B05, 42B08.
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 (L, ξ(t)) classes using Cesàro and (generalized) Nörlund single summability methods by a number of researchers like Alexits , Sahney and Goel , Qureshi and Neha , Quershi [7, 8], Chandra , Khan , Leindler  and… (More)
In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α, r), 1 ≤ r < ∞ and the weighted class W (Lr, ξ(t)), 1 ≤ r < ∞ by (C, 2)(E, 1) product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.
A new theorem on almost generalized Nörlund summability of conjugate series of Fourier series has been established under a very general condition. 2000 Mathematics Subject Classification. Primary 42B05, 42B08.
H. K. Nigam and Ajay Sharma Department of Mathematics, Faculty of Engineering & Technology, Mody Institute of Technology and Science (Deemed University), Laxmangarh, Sikar (Rajasthan) 332311, India Correspondence should be addressed to Ajay Sharma, email@example.com Received 7 November 2008; Revised 17 March 2009; Accepted 30 March 2009… (More)
In this paper, a quite new theorem on almost summability of Fourier-Jacobi series has been established. Our theorem extends and generalizes all previously known results of this line of work. Full text