Trigonometric Approximation of Signals (Functions) Belonging to the Lip(ξ(t),r),(r>1)-Class by (E,q) (q>0)-Means of the Conjugate Series of Its Fourier Series

Various investigators such as Khan ([1-4]), Khan and Ram [5], Chandra [6,7], Leindler [8], Mishra et al. [9], Mishra [10], Mittal et al. [11], Mittal, Rhoades and Mishra [12], Mittal and Mishra [13], Rhoades et al. [14] have determined the degree of approximation of 2π-periodic signals (functions) belonging to various classes Lip   , Lip r   Lip     , r t  , and W L of functions through trigonometric Fourier approximation (TFA) using different summability matrices with monotone rows. Recently, Mittal et al. [15], Mishra and Mishra [16], Mishra [17] have obtained the degree of approximation of signals belonging to    , t r    , Lip r  -class by general summability matrix, which generalizes the results of Leindler [8] and some of the results of Chandra [7] by dropping monotonicity on the elements of the matrix rows (that is, weakening the conditions on the filter, we improve the quality of digital filter). In this paper, a theorem concerning the degree of approximation of the conjugate of a signal (function) f belonging to     , Lip t r    , E q     , Lip t r    , E q class by summability of conjugate series of its Fourier series has been established which in turn generalizes the results of Chandra [7] and Shukla [18].