Topology and Approximate Fixed Points

Format: Paperback / softback
Length: 251 pages
Publication date: 27 January 2023
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the intricate realm of approximate fixed point theory, exploring its applications across diverse classes of topological spaces and maps. It offers a thorough and up-to-date treatment of the subject, catering to a wide range of topologies and maps. The content encompasses both well-known and recent results in topology, along with cutting-edge developments in approximate fixed point theory. The work begins by establishing a foundational framework in topological spaces, focusing on key concepts such as topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces are also explored, along with their fundamental properties and topologies. Fundamental principles, including the Hahn-Banach theorem on extensions of linear functionals, the Banach open mapping theorem, the Banach-Steinhaus uniform boundedness principle, and Baire categories, are discussed in depth. Weak topologies and their remarkable properties are explored, encompassing theorems by Eberlein-Smulian, Goldstine, Kakutani, James, and Grothendieck. These principles include reflexive Banach spaces, l_1- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space, weak* topology of its dual, and the Fréchet-Urysohn property. The subsequent chapters delve into various almost fixed point results, highlighting techniques for reaching or approximating the unique fixed point of a strictly contractive mapping in a spherically complete ultrametric space. Additionally, synthetic approaches to fixed point problems involving regular-global-inf functions are introduced. The book concludes with a study of problems involving the approximate fixed point property on an ambient space with different topologies. By providing a solid background and presenting the latest advancements in the field, this book serves as a valuable resource for researchers and practitioners in mathematics, particularly in the areas of topology, functional analysis, and applied mathematics.

Weight: 415g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030922061
Edition number: 1st ed. 2022