The Theory of Inequalities began its development from the time when C.
F. GACSS, A. L. CATCHY and P. L. CEBYSEY, to mention only the most
important, laid the theoretical foundation for approximative meth- ods.
Around the end of the 19th and the beginning of the 20th century,
numerous inequalities were proyed, some of which became classic, while
most remained as isolated and unconnected results. It is almost
generally acknowledged that the classic work "Inequali- ties" by G. H.
HARDY, J. E. LITTLEWOOD and G. POLYA, which appeared in 1934,
transformed the field of inequalities from a collection of isolated
formulas into a systematic discipline. The modern Theory of
Inequalities, as well as the continuing and growing interest in this
field, undoubtedly stem from this work. The second English edition of
this book, published in 1952, was unchanged except for three appendices,
totalling 10 pages, added at the end of the book. Today inequalities
playa significant role in all fields of mathematics, and they present a
very active and attractive field of research. J. DIEUDONNE, in his book
"Calcullnfinitesimal" (Paris 1968), attri- buted special significance to
inequalities, adopting the method of exposi- tion characterized by
"majorer, minorer, approcher". Since 1934 a multitude of papers devoted
to inequalities have been published: in some of them new inequalities
were discovered, in others classical inequalities, vere sharpened or
extended, various inequalities, vere linked by finding their common
source, while some other papers gave a large number of miscellaneous
applications.