# Faton M. Berisha and Muharrem Q. Berisha

### Faculty of Mathematical and Natural Sciences, University of Prishtina, Prishtina,Kosova

For a sequence of real or complex numbers and a given sequence the linear operator is defined by Theorem 1. Let be a convergent real or complex trigonometric series and a sequence of real or complex numbers such that . Then the following equation holds true (1)

where are .

Corollary 1. If there exist the finite limits  , then series on the left-hand side of (1) converges faster then the series

on the right-hand side.

The acceleration of convergence is increased with the value of p.

Example 1. Let . Then Obviously, for every integer p the sequence satisfies the conditions of Corollary 1. In particular, in order to calculate the approximate sum of the series with an error not greater than we must compute the sum of first 9 terms. Applying the transformation (1), the same accuracy is obtained by computing the sum of 5 terms for , 3 terms for and 1 term for .