Topology and Approximate Fixed Points (Developments in Mathematics, 71)

Description: Topology and Approximate Fixed Points (Developments in Mathematics, 71) [Hardcover] Ben Amar, Afif and O'Regan, Donal Product Overview This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory. This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces―and fundamental properties of their topologies―are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included areweak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak topology of its dual, and the Fréchet-Urysohn property. The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies. By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed pointtheory. Read more Details Publisher ‏ : ‎ Springer; 1st ed. 2022 edition (January 26, 2022) Language ‏ : ‎ English Hardcover ‏ : ‎ 264 pages ISBN-10 ‏ : ‎ 3030922030 ISBN-13 ‏ : ‎ 30 Item Weight ‏ : ‎ 1.26 pounds Dimensions ‏ : ‎ 6.14 x 0.63 x 9.21 inches Best Sellers Rank: #7,103,991 in Books (See Top 100 in Books) #1,370 in Functional Analysis Mathematics #1,733 in Topology (Books) #29,861 in Mathematics (Books) #1,370 in Functional Analysis Mathematics #1,733 in Topology (Books) We have been selling used books since 2012, and we've learned that the most important thing is doing good business. Honesty is our policy. Free Shipping We ship worldwide. We have multiple warehouses around the world, so please note the extended handling time on certain listings.

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