DEGREE OF APPROXIMATION OF FUNCTIONS BELONGING TO LIPα CLASS AND WEIGHTED (L,ξ(t)) CLASS BY PRODUCT SUMMABILITY METHOD

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 [1], Sahney and Goel [11], Qureshi and Neha [9], Quershi [7, 8], Chandra [2], Khan [4], Leindler [5] and Rhoades [10]. But till now no work seems to have been done so far in the direction of present work. Therefore, in present paper, two quite new results on degree of approximation of functions f ∈ Lipα and f ∈W (L, ξ(t)) class by (E,1)(C,1) product summability means of Fourier series have been obtained.