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Distortion Theorems in Relation to Linear Integral Operators (Paperback, Softcover reprint of the original 1st ed. 1996)
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Distortion Theorems in Relation to Linear Integral Operators (Paperback, Softcover reprint of the original 1st ed. 1996)
Series: Mathematics and Its Applications, 385
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The present monograph consists of two parts. Before Part I, a
chapter of introduction is supplemented, where an overview of the
whole volume is given for reader's convenience. The former part is
devoted mainly to expose linear inte gral operators introduced by
the author. Several properties of the operators are established,
and specializations as well as generalizations are attempted
variously in order to make use them in the latter part. As compared
with the former part, the latter part is de voted mainly to develop
several kinds of distortions under actions of integral operators
for various familiar function also absolute modulus. real part.
range. length and area. an gular derivative, etc. Besides them,
distortions on the class of univalent functions and its subclasses,
Caratheodory class as well as distortions by a differential
operator are dealt with. Related differential operators play also
active roles. Many illustrative examples will be inserted in order
to help understanding of the general statements. The basic
materials in this monograph are taken from a series of researches
performed by the author himself chiefly in the past two decades.
While the themes of the papers pub lished hitherto are necessarily
not arranged chronologically Preface viii and systematically, the
author makes here an effort to ar range them as, orderly as
possible. In attaching the import ance of the self-containedness to
the book, some of unfamil iar subjects will also be inserted and,
moreover, be wholly accompanied by their respective proofs, though
unrelated they may be."
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