Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness
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Beschreibung
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.
Presents a survey of results concerning classical measures of noncompactness and their role in fixed-point theory and operator theory Discusses the applications to the solvability of nonlinear integral equations and characterization of compact matrix operators Collects and presents sufficient conditions for the solvability of differential equations, integral equations, and functional integral equations Highlights some of the real-world practical problems from different branches of the applied sciences Includes supplementary material: sn.pub/extras
Autor*in
Józef Banaś
Themen in »Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness«
Noncompactness Integral equations Differential equations Fixed Points Banach Space ordinary differential equations