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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.
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.
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