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Elementary Fixed Point Theorems (Hardcover, 1st ed. 2018)
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Elementary Fixed Point Theorems (Hardcover, 1st ed. 2018)
Series: Forum for Interdisciplinary Mathematics
Expected to ship within 12 - 17 working days
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This book provides a primary resource in basic fixed-point theorems
due to Banach, Brouwer, Schauder and Tarski and their applications.
Key topics covered include Sharkovsky's theorem on periodic points,
Thron's results on the convergence of certain real iterates,
Shield's common fixed theorem for a commuting family of analytic
functions and Bergweiler's existence theorem on fixed points of the
composition of certain meromorphic functions with transcendental
entire functions. Generalizations of Tarski's theorem by Merrifield
and Stein and Abian's proof of the equivalence of Bourbaki-Zermelo
fixed-point theorem and the Axiom of Choice are described in the
setting of posets. A detailed treatment of Ward's theory of
partially ordered topological spaces culminates in Sherrer
fixed-point theorem. It elaborates Manka's proof of the fixed-point
property of arcwise connected hereditarily unicoherent continua,
based on the connection he observed between set theory and
fixed-point theory via a certain partial order. Contraction
principle is provided with two proofs: one due to Palais and the
other due to Barranga. Applications of the contraction principle
include the proofs of algebraic Weierstrass preparation theorem, a
Cauchy-Kowalevsky theorem for partial differential equations and
the central limit theorem. It also provides a proof of the converse
of the contraction principle due to Jachymski, a proof of fixed
point theorem for continuous generalized contractions, a proof of
Browder-Gohde-Kirk fixed point theorem, a proof of Stalling's
generalization of Brouwer's theorem, examine Caristi's fixed point
theorem, and highlights Kakutani's theorems on common fixed points
and their applications.
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