Furuichi S., Moradi H.R. Advances in Mathematical Inequalities

Berlin: Walter de Gruyter, 2020. — 268 p. — ISBN: 311064343X.Mathematical inequalities are essential tools in mathematics, natural science and engineering. This book gives an overview on recent advances. Some generalizations and improvements for the classical and well-known inequalities are described. The book may be used by researchers in different branches of mathematical and functional analysis, where the theory of Hilbert spaces is of relevance. Since it is self-contained and all the results are entirely proved, the work may also be used by graduate students interested in theory of inequalities and its applications. Applications of the inequalities to entropy theory and quantum physics are also included.Introduction and preliminaries.
Refinements and reverses for Young inequality.
Inequalities related to means.
Norm inequalities and trace inequalities.
Convex functions and Jensen inequality.
Reverses for classical inequalities.
Applications to entropy theory.
Miscellaneous topics.True PDF