Valeri Obukhovskii & Boris Gel'Man Knihy

The theory of multivalued maps and differential inclusions are interconnected and rapidly evolving areas of contemporary mathematics, with significant applications in control theory, optimization, calculus of variations, non-smooth and convex analysis, game theory, and mathematical economics. This book offers a user-friendly, self-contained introduction to these subjects, targeting senior students and beginners. It serves both pure mathematics enthusiasts and those interested in practical applications. Chapter 0 provides essential definitions and fundamental results in topology. Chapter 1 illustrates the emergence of multivalued maps through examples from various mathematical fields, explores their properties, and concludes with measurable multivalued functions. Chapter 2 focuses on fixed point theory for multivalued maps. Chapter 3 delves into differential inclusions and their relevance in control theory. The final Chapter 4 discusses applications in dynamical systems, game theory, and mathematical economics. The book concludes with bibliographic commentaries and additional resources that enhance the topics covered, alongside an extensive bibliography of over 400 items, ranging from foundational works to recent research.