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Full Description
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.
Contents
Measures of Noncompactness in the Space of Continuous and Bounded Functions Defined on the Real Half-Axis.- Measures of Noncompactness and Their Applications.- On Some Results Using Measures of Noncompactness.- Space of Functions with Growths Tempered by a Modulus of Continuity.- Measure of Noncompactness in Functional Fractional Calculus.- Measures of Weak Noncompactness and Fixed Points.- The Class of F-Contraction Mappings with a Measure of Noncompactness.- On The Measure of Non-Compactness in Banach Spaces and Application to the Theory of Differential and Integral Equations.- Partial Hadamard-Stieltjes Fractional Integral Equations in Banach Spaces.- Boundary Value Problems for Fractional Differential Equations and Inclusions in Banach Spaces.- On the Aronszajn Property for Differential Equations of Fractional Order in Banach Spaces.- On the Qualitative Behaviors of Nonlinear Functional Differential Systems of Third Order.- On the Approximation of Solutions to a Fixed Point Problem with Inequality Constraints in a Banach Space Partially Ordered by a Cone.- A Short Survey on Dislocated Metric Spaces via Fixed Point Theory.
