On L1-Convergence of Certain Trigonometric Series with Special Coefficients

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, I 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 1 L -convergence of modified cosine sums introduced by Kumari and Ram in 1988 with class S  of coefficient sequences. In chapter III, I have studied the 1 L -convergence of modified cosine sums introduced by Kumari and Ram under a new class   r S of coefficient sequences. In chapter IV, I have studied the 1 L -convergence of modified cosine sums introduced by Rees-Stanojevic with class ** r S . I have also studied the 1 L -convergence of the th r derivative of the cosine sums under a class ** r S .