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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Topology and Approximate Fixed Points (Hardcover, 1st ed. 2022)
Loot Price: R1,702
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Topology and Approximate Fixed Points (Hardcover, 1st ed. 2022)
Series: Developments in Mathematics, 71
Expected to ship within 10 - 15 working days
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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 are weak 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
Frechet-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 point theory.
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