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Summability Theory and Its Applications explains various aspects of
summability and demonstrates its applications in a rigorous and
coherent manner. The content can readily serve as a reference or as
a useful series of lecture notes on the subject. This substantially
revised new edition includes brand new material across several
chapters as well as several corrections, including: the addition of
the domain of Cesaro matrix C(m) of order m in the classical
sequence spaces to Chapter 4; and introducing the domain of
four-dimensional binomial matrix in the spaces of bounded,
convergent in the Pringsheim's sense, both convergent in the
Pringsheim's sense and bounded, and regularly convergent double
sequences, in Chapter 7. Features Investigates different types of
summable spaces and computes their dual Suitable for graduate
students and researchers with a (special) interest in spaces of
single and double sequences, matrix transformations and domains of
triangle matrices Can serve as a reference or as supplementary
reading in a computational physics course, or as a key text for
special Analysis seminars.
Double Sequence Spaces and Four-Dimensional Matrices provides
readers with a clear introduction to the spaces of double sequences
and series, as well as their properties. The book then goes beyond
this to investigate paranormed double sequence spaces and their
algebraic and topological properties, triangle matrices and their
domains in certain spaces of double sequences, dual spaces of
double sequence spaces, and matrix transformations between double
sequence spaces and related topics. Each chapter contains a
conclusion section highlighting the importance of results and
pointing out possible new ideas that can be studied further.
Features Suitable for students at graduate or post-graduate level
and researchers Investigates different types of summable spaces and
computes their duals Characterizes several four-dimensional matrix
classes transforming one summable space into other Discusses
several algebraic and topological properties of new sequence spaces
generated by the domain of triangles.
Presents Sequence Spaces, their properties and Summability methods,
which provides the foundation of every course in analysis Provides
different points of view in one volume, e.g. their topological
properties, geometry and summability, fuzzy valued study and more
Aimed at both experts and non-experts with an interest in getting
acquainted with sequence space, matrix transformations and their
applications Consists of several new results which are part of the
recent research on these topics Covers Fuzzy Valued sequences,
which is an important topic and exhibits the study of sequence
spaces in fuzzy settings
The aim of Summable Spaces and Their Duals, Matrix Transformations
and Geometric Properties is to discuss primarily about different
kinds of summable spaces, compute their duals and then characterize
several matrix classes transforming one summable space into other.
The book also discusses several geometric properties of summable
spaces, as well as dealing with the construction of summable spaces
using Orlicz functions, and explores several structural properties
of such spaces. Each chapter contains a conclusion section
highlighting the importance of results, and points the reader in
the direction of possible new ideas for further study. Features
Suitable for graduate schools, graduate students, researchers and
faculty, and could be used as a key text for special Analysis
seminars Investigates different types of summable spaces and
computes their duals Characterizes several matrix classes
transforming one summable space into other Discusses several
geometric properties of summable spaces Examines several possible
generalizations of Orlicz sequence spaces
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.
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