Logarithmic summability methods and Tauberian theorems

This thesis consists of six chapters. The first chapter is devoted to the introduction. In the second chapter, the basic definitions, notations and lemmas used in the thesis are given and classical Tauberian theorems are examined. In the third chapter, Tauberian theorems for the logarithmic power series summability method (L) are proved. In the fourth chapter, the generalized logarithmic power series method (L,m) is defined and the results in the third chapter are extended to (L,m) summability. In the fifth chapter, the concepts of statistical convergence and statistical (l,m) summability are introduced and related Tauberian theorems are investigated. In the sixth chapter, the concept of subsequential convergence is discussed in detail and sufficient Tauberian conditions are obtained to retrieve subsequential convergence of a sequence from its boundedness.