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.
General
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