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The book is devoted to dynamic inequalities of Hardy type and
extensions and generalizations via convexity on a time scale T. In
particular, the book contains the time scale versions of classical
Hardy type inequalities, Hardy and Littlewood type inequalities,
Hardy-Knopp type inequalities via convexity, Copson type
inequalities, Copson-Beesack type inequalities, Liendeler type
inequalities, Levinson type inequalities and Pachpatte type
inequalities, Bennett type inequalities, Chan type inequalities,
and Hardy type inequalities with two different weight functions.
These dynamic inequalities contain the classical continuous and
discrete inequalities as special cases when T = R and T = N and can
be extended to different types of inequalities on different time
scales such as T = hN, h > 0, T = qN for q > 1, etc.In this
book the authors followed the history and development of these
inequalities. Each section in self-contained and one can see the
relationship between the time scale versions of the inequalities
and the classical ones. To the best of the authors' knowledge this
is the first book devoted to Hardy-typeinequalities and their
extensions on time scales.
The book is devoted to dynamic inequalities of Hardy type and
extensions and generalizations via convexity on a time scale T. In
particular, the book contains the time scale versions of classical
Hardy type inequalities, Hardy and Littlewood type inequalities,
Hardy-Knopp type inequalities via convexity, Copson type
inequalities, Copson-Beesack type inequalities, Liendeler type
inequalities, Levinson type inequalities and Pachpatte type
inequalities, Bennett type inequalities, Chan type inequalities,
and Hardy type inequalities with two different weight functions.
These dynamic inequalities contain the classical continuous and
discrete inequalities as special cases when T = R and T = N and can
be extended to different types of inequalities on different time
scales such as T = hN, h > 0, T = qN for q > 1, etc.In this
book the authors followed the history and development of these
inequalities. Each section in self-contained and one can see the
relationship between the time scale versions of the inequalities
and the classical ones. To the best of the authors' knowledge this
is the first book devoted to Hardy-typeinequalities and their
extensions on time scales.
Environmental variation plays an important role in many biological
and ecological dynamical systems. This monograph focuses on the
study of oscillation and the stability of delay models occurring in
biology. The book presents recent research results on the
qualitative behavior of mathematical models under different
physical and environmental conditions, covering dynamics including
the distribution and consumption of food. Researchers in the fields
of mathematical modeling, mathematical biology, and population
dynamics will be particularly interested in this material.
Environmental variation plays an important role in many biological
and ecological dynamical systems. This monograph focuses on the
study of oscillation and the stability of delay models occurring in
biology. The book presents recent research results on the
qualitative behavior of mathematical models under different
physical and environmental conditions, covering dynamics including
the distribution and consumption of food. Researchers in the fields
of mathematical modeling, mathematical biology, and population
dynamics will be particularly interested in this material.
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