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Title
Convergence methods for double sequences and applications [electronic resource] / M. Mursaleen, S.A. Mohiuddine.
ISBN
9788132216117 electronic book
8132216113 electronic book
9788132216100
Published
New Delhi : Springer, 2014.
Language
English
Description
1 online resource (ix, 171 pages)
Item Number
10.1007/978-81-322-1611-7 doi
Call Number
QA295
Dewey Decimal Classification
515/.24
Summary
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.
Bibliography, etc. Note
Includes bibliographical references.
Access Note
Access limited to authorized users.
Source of Description
Description based on online resource; title from PDF title page (SpringerLink, viewed October 21, 2013).
Chapter 1: Almost and statistical convergence of ordinary sequences: A preview
Chapter 2: Almost convergence of double sequences
Chapter 3: Almost regular matrices
Chapter 4: Absolute almost convergence of double sequences
Chapter 5: Almost convergence and core theorems
Chapter 6: Application of almost convergence in approximation theorems for functions of two variables
Chapter 7: Statistical convergence of double sequences
Chapter 8: Statistical approximation of positive linear operators
Chapter 9: Double series and convergence tests.
