A Study of Generalized Convergence Criteria

Abstract

The title of this thesis A Study of Generalized Convergence Criteriaquot has been written for the submission to Chandigarh University in partial fulllment of the requirement of the degree of Doctor of Philosophy in Mathematics. newlineSequence has a signicant role in the area of Analysis. Sequence spaces play an essential role in various elds of Real Analysis, Complex Analysis, Functional Analysis and Topology. The convergence of sequences has always remained a subject of interest to the researchers. Later on, Fast[47] has introduced a new concept of convergence named as statistical conver- gence more generalized than the usual convergence. It has been studied by many researchers for various types of sequences in dierent sequence space setups like locally convex space[86], probabilistic normed space[72], intuitionistic fuzzy normed space[73] etc. For more work re- lated to statistical convergence, one may refer to [107],[111], [112], [24] and [94]. A sequence space is a vector space whose elements are innite sequences of real or complex numbers. Sequence spaces are typically equipped with a norm, or at least the structure of a topological vector space. newlineIn this thesis, we studied generalized convergence for the spaces where uncertainty and inexactness occurs. We dened some new notions for rough convergence and studied some of the topological and algebraic properties of these new resulting on some spaces. This thesis comprises of six chapters and each chapter is divided into sections. newline newline