Integrability and L1-Convergence of Certain Cosine SUMS

Abstract

The work presented in this dissertation has been divided into four chapters. The first chapter is introductory. In this chapter, apart from setting up the notations and terminology to be used in sequel, we have presented some known results interrelated to our results along with a brief plan of our results presented in the subsequent chapters. The purpose of chapter II is to study the integrability and 1 L -convergence of Rees and Stanojevic cosine sum under the Class C of coefficient sequences. In chapter III, I studied the results concerning the 1 L -convergence of cosine trigonometric series under the class 2 S of coefficient sequences which is equivalent to class S of Sidon. In chapter IV, I have studied the generalization of the results of Garrett and Stanojevic by considering the class (BV )m instead of class BV .