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Since the elassie work on inequalities by HARDY, LITTLEWOOD, and
P6LYA in 1934, an enonnous amount of effort has been devoted to the
sharpening and extension of the elassieal inequalities, to the
discovery of new types of inequalities, and to the application of
inqualities in many parts of analysis. As examples, let us eite the
fields of ordinary and partial differential equations, whieh are
dominated by inequalities and variational prineiples involving
functions and their derivatives; the many applications of linear
inequalities to game theory and mathe- matieal economics, which
have triggered a renewed interest in con- vexity and moment-space
theory; and the growing uses of digital com- puters, which have
given impetus to a systematie study of error esti- mates involving
much sophisticated matrix theory and operator theory. The results
presented in the following pages reflect to some extent these
ramifications of inequalities into contiguous regions of analysis,
but to a greater extent our concem is with inequalities in their
native habitat. Since it is elearly impossible to give a connected
account of the burst of analytic activity of the last twenty-five
years centering about inequalities, we have d. eeided to limit our
attention to those topies that have particularly delighted and
intrigued us, and to the study of whieh we have contributed.
Additional Contributing Authors Include E. T. Bell, Richard
Bellman, Herbert Busemann, And Many Others.
Additional Contributing Authors Include E. T. Bell, Richard
Bellman, Herbert Busemann, And Many Others.
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