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.

In a previous paper [9], some classes of triangular matrix transformations between the series spaces summable by absolute weighted summability methods were characterized. present paper, we extend these to four dimensional matrices and double methods.

A blend of matrix summability and Euler transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties this space finally, some inclusion relations are presented.

Rhoades and Sava¸s [6],[11] established necessary for inclusions of the absolute matrix summabilities under additional conditions. In this paper we determine or su¢ cient conditions some classes in…nite matrices, using get more general applied to all matrices.

In this paper, we prove two theorems on ∣A∣k, 1 ≤ k ≤ 2, summability of orthogonal series. The first one gives a sufficient condition under which an orthogonal series is absolutely summable almost everywhere, and the second one, is a general theorem, which also gives a sufficient condition so that an orthogonal series is absolutely summable almost everywhere, but it involves a positive numerica...

In this paper we prove a general theorem on |A; δ|k -summability factors of infinite series under suitable conditions by using an almost increasing sequence, where A is a lower triangular matrix with non-negative entries. Also, we deduce a similar result for the weighted mean method. c © 2007 Elsevier Ltd. All rights reserved.

In this paper, we prove a simple inequality which plays important role in the summability theory, matrix operators theory, approximation theory, and also provides great convenience in computations. As a corollary, we give the well known results of [1,2,5] under some simpler conditions, and a very short and different.proofs of results in [6,7] .