Feyzi Başar

Mohammad Mursaleen

This book is aimed at both experts and non-experts with an interest in getting acquainted with sequence spaces, matrix transformations and their applications. It consists of several new results which are part of the recent research on these topics. It provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more. This book presents the important role sequences and series play in everyday life, it covers geometry of Banach Sequence Spaces, it discusses the importance of generalized limit, it offers spectrum and fine spectrum of several linear operators and includes fuzzy valued sequences which exhibits the study of sequence spaces in fuzzy settings. This book is the main attraction for those who work in Sequence Spaces, Summability Theory and would also serve as a good source of reference for those involved with any topic of Real or Functional Analysis.

Topics in Modern Summability Theory

Sequence Spaces

S. A. Mohiuddine

This book exclusively deals with the study of almost convergence and statistical convergence of double sequences. The notion of “almost convergence” is perhaps the most useful notion in order to obtain a weak limit of a bounded non-convergent sequence. There is another notion of convergence known as the “statistical convergence”, introduced by H. Fast, which is an extension of the usual concept of sequential limits. This concept arises as an example of “convergence in density” which is also studied as a summability method. Even unbounded sequences can be dealt with by using this method. The book also discusses the applications of these non-matrix methods in approximation theory. Written in a self-contained style, the book discusses in detail the methods of almost convergence and statistical convergence for double sequences along with applications and suitable examples. The last chapter is devoted to the study convergence of double series and describes various convergence tests analogous to those of single sequences. In addition to applications in approximation theory, the results are expected to find application in many other areas of pure and applied mathematics such as mathematical analysis, probability, fixed point theory and statistics.

Mohammad Mursaleen

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