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 On Some Integral Inequalities of Hilbert's Type

Show simple item record  عباس كامل صادق شراب 6/12/2020 6/12/2020 2020-12-14T11:07:23Z 6/12/2020 2020-12-14T11:07:23Z 12/12/2013
dc.description.abstract In the last few years, the field of integral and discrete inequalities has continued to develop rapidly. Inequalities are one of the most important instruments in many branches of mathematics such as functional analysis, theory of differential and integrals equations, probability theory, etc. They are also useful in mechanics, physics and other sciences. This thesis is concerned, in a unified manner, with some but important integral types of inequalities, mainly with Hilbert's and Hardy-Hilbert's inequalities. We pick up a direction recently followed by a number of mathematicians like: Youngjin Li, Yu Miao, Bing He, and You Qian (see [6], [15], [14]) and study, analyze and make some modifications on those inequalities. In this thesis, we present a detailed study of an important type of inequalities called Hilbert's Inequalities in two dimensions with introducing its various generalizations like Hardy's inequalities. Extending those inequalities to multiple integrals as well as reviewing the corresponding inequalities in discrete form. Attention is paid to study the strict case and establish the best constants for Hilbert's type inequalities and we also prove the equivalent form for these inequalities. en_US
dc.language.iso en_US en_US
dc.publisher Batch2 en_US
dc.title  On Some Integral Inequalities of Hilbert's Type en_US
dc.type Thesis en_US

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