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Applications of measures of noncompactness to various problems. (English) Zbl 0619.47044

The book is a continuation of the author’s and K. Goebel’s monograph ”Measures of noncompactness in Banach spaces” (this Zbl 0441.47056) and contains implementations of this concept to various problems of analysis. The chapters deal successively with applications in the approximation theory by regular functions, the geometry of Banach spaces, the existence of solutions for operator equations in the space of continuous or integrable functions on a bounded interval, functional- integral and differential equations as well as nonlinear stochastic equations with deviated argument.

Due to his rich experience, the author managed in this very readable work to enlighten the role of measures of noncompactness, notion of Polish origin, to the present functional analysis and operator theory. The list of references includes 159 items, among which 22 belong to the author and is collaborators.

Reviewer: D.Pascali
47H09Mappings defined by “shrinking” properties
47J05Equations involving nonlinear operators (general)
34G20Nonlinear ODE in abstract spaces