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This book collects papers on major topics in fixed point theory and
its applications. Each chapter is accompanied by basic notions,
mathematical preliminaries and proofs of the main results. The book
discusses common fixed point theory, convergence theorems, split
variational inclusion problems and fixed point problems for
asymptotically nonexpansive semigroups; fixed point property and
almost fixed point property in digital spaces, nonexpansive
semigroups over CAT( ) spaces, measures of noncompactness, integral
equations, the study of fixed points that are zeros of a given
function, best proximity point theory, monotone mappings in modular
function spaces, fuzzy contractive mappings, ordered hyperbolic
metric spaces, generalized contractions in b-metric spaces,
multi-tupled fixed points, functional equations in dynamic
programming and Picard operators. This book addresses the
mathematical community working with methods and tools of nonlinear
analysis. It also serves as a reference, source for examples and
new approaches associated with fixed point theory and its
applications for a wide audience including graduate students and
researchers.
This book deals with the study of sequence spaces, matrix
transformations, measures of noncompactness and their various
applications. The notion of measure of noncompactness is one of the
most useful ones available and has many applications. The book
discusses some of the existence results for various types of
differential and integral equations with the help of measures of
noncompactness; in particular, the Hausdorff measure of
noncompactness has been applied to obtain necessary and sufficient
conditions for matrix operators between BK spaces to be compact
operators.
The book consists of eight self-contained chapters. Chapter 1
discusses the theory of FK spaces and Chapter 2 various duals of
sequence spaces, which are used to characterize the matrix classes
between these sequence spaces (FK and BK spaces) in Chapters 3 and
4. Chapter 5 studies the notion of a measure of noncompactness and
its properties. The techniques associated with measures of
noncompactness are applied to characterize the compact matrix
operators in Chapters 6. In Chapters 7 and 8, some of the existence
results are discussed for various types of differential and
integral equations, which are obtained with the help of
argumentations based on compactness conditions.
This book offers a comprehensive treatment of the theory of
measures of noncompactness. It discusses various applications of
the theory of measures of noncompactness, in particular, by
addressing the results and methods of fixed-point theory. The
concept of a measure of noncompactness is very useful for the
mathematical community working in nonlinear analysis. Both these
theories are especially useful in investigations connected with
differential equations, integral equations, functional integral
equations and optimization theory. Thus, one of the book's central
goals is to collect and present sufficient conditions for the
solvability of such equations. The results are established in
miscellaneous function spaces, and particular attention is paid to
fractional calculus.
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
This book collects papers on major topics in fixed point theory and
its applications. Each chapter is accompanied by basic notions,
mathematical preliminaries and proofs of the main results. The book
discusses common fixed point theory, convergence theorems, split
variational inclusion problems and fixed point problems for
asymptotically nonexpansive semigroups; fixed point property and
almost fixed point property in digital spaces, nonexpansive
semigroups over CAT( ) spaces, measures of noncompactness, integral
equations, the study of fixed points that are zeros of a given
function, best proximity point theory, monotone mappings in modular
function spaces, fuzzy contractive mappings, ordered hyperbolic
metric spaces, generalized contractions in b-metric spaces,
multi-tupled fixed points, functional equations in dynamic
programming and Picard operators. This book addresses the
mathematical community working with methods and tools of nonlinear
analysis. It also serves as a reference, source for examples and
new approaches associated with fixed point theory and its
applications for a wide audience including graduate students and
researchers.
This book offers a comprehensive treatment of the theory of
measures of noncompactness. It discusses various applications of
the theory of measures of noncompactness, in particular, by
addressing the results and methods of fixed-point theory. The
concept of a measure of noncompactness is very useful for the
mathematical community working in nonlinear analysis. Both these
theories are especially useful in investigations connected with
differential equations, integral equations, functional integral
equations and optimization theory. Thus, one of the book's central
goals is to collect and present sufficient conditions for the
solvability of such equations. The results are established in
miscellaneous function spaces, and particular attention is paid to
fractional calculus.
This book deals with the study of sequence spaces, matrix
transformations, measures of noncompactness and their various
applications. The notion of measure of noncompactness is one of the
most useful ones available and has many applications. The book
discusses some of the existence results for various types of
differential and integral equations with the help of measures of
noncompactness; in particular, the Hausdorff measure of
noncompactness has been applied to obtain necessary and sufficient
conditions for matrix operators between BK spaces to be compact
operators. The book consists of eight self-contained chapters.
Chapter 1 discusses the theory of FK spaces and Chapter 2 various
duals of sequence spaces, which are used to characterize the matrix
classes between these sequence spaces (FK and BK spaces) in
Chapters 3 and 4. Chapter 5 studies the notion of a measure of
noncompactness and its properties. The techniques associated with
measures of noncompactness are applied to characterize the compact
matrix operators in Chapters 6. In Chapters 7 and 8, some of the
existence results are discussed for various types of differential
and integral equations, which are obtained with the help of
argumentations based on compactness conditions.
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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