On 1Ll - convergence of modified trigonometric sums

Abstract

The present dissertation entitled, “ON 1 L - CONVERGENCE OF MODIFIED TRIGONOMETRIC SUMS”, contains a brief account of the study carried out by me on 1 L - convergence of trigonometric series under the supervision of Dr. S.S. Bhatia, Professor, School of Mathematics and computer Applications, Thapar University, Patiala. The whole work presented in this dissertation is divided into four chapters. Chapter-I is introductory. In this chapter, apart from setting up the notations and terminology to be used in subsequent chapters, I have presented some known results related with our results along with a brief plan of the results presented in chapters to follow. The aim of chapter II is to study the 1 L -convergence of modified cosine sums of Kumari and Ram given in 1988 for the class S of Sidon. Chapter III is devoted to the study of 1 L - convergence of th r derivatives of the modified cosine sums of Kumari and Ram under class r S of coefficient sequences introduced by Tomovski. In chapter IV, the 1 L - convergence of modified cosine sums introduced by Kumari and Ram for the class of the coefficient sequence given by Telijakovski have been studied. References of various publications cited in the present dissertation have been reported towards the end of the dissertation.