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It was noted in the preface of the book "Inequalities Involving
Functions and Their Integrals and Derivatives," Kluwer Academic
Publishers, 1991, by D.S. Mitrinovic, J.E. Pecaric and A.M. Fink;
since the writing of the classical book by Hardy, Littlewood and
Polya (1934), the subject of differential and integral inequalities
has grown by about 800%. Ten years on, we can confidently assert
that this growth will increase even more significantly. Twenty
pages of Chapter XV in the above mentioned book are devoted to
integral inequalities involving functions with bounded derivatives,
or, Ostrowski type inequalities. This is now itself a special
domain of the Theory of Inequalities with many powerful results and
a large number of applications in Numerical Integration,
Probability Theory and Statistics, Information Theory and Integral
Operator Theory. The main aim of the present book, jointly written
by the members of the Vic toria University node of RGMIA (Research
Group in Mathematical Inequali ties and Applications, http: I
/rgmia. vu. edu. au) and Th. M. Rassias, is to present a selected
number of results on Ostrowski type inequalities. Results for
univariate and multivariate real functions and their natural
applications in the error analysis of numerical quadrature for both
simple and multiple integrals as well as for the Riemann-Stieltjes
integral are given."
It was noted in the preface of the book "Inequalities Involving
Functions and Their Integrals and Derivatives," Kluwer Academic
Publishers, 1991, by D.S. Mitrinovic, J.E. Pecaric and A.M. Fink;
since the writing of the classical book by Hardy, Littlewood and
Polya (1934), the subject of differential and integral inequalities
has grown by about 800%. Ten years on, we can confidently assert
that this growth will increase even more significantly. Twenty
pages of Chapter XV in the above mentioned book are devoted to
integral inequalities involving functions with bounded derivatives,
or, Ostrowski type inequalities. This is now itself a special
domain of the Theory of Inequalities with many powerful results and
a large number of applications in Numerical Integration,
Probability Theory and Statistics, Information Theory and Integral
Operator Theory. The main aim of the present book, jointly written
by the members of the Vic toria University node of RGMIA (Research
Group in Mathematical Inequali ties and Applications, http: I
/rgmia. vu. edu. au) and Th. M. Rassias, is to present a selected
number of results on Ostrowski type inequalities. Results for
univariate and multivariate real functions and their natural
applications in the error analysis of numerical quadrature for both
simple and multiple integrals as well as for the Riemann-Stieltjes
integral are given."
Inequality Theory & Applications
This book introduces and exchanges recent innovative topics on the
areas of fixed point theory, convex and set-valued analysis,
variational inequality and complementarity problem theory,
non-linear ergodic theory, difference, differential and integral
equations, control and optimisation theory, dynamic system theory,
inequality theory, stochastic analysis and probability theory, and
their applications.
This book introduces and exchanges recent innovative topics on the
areas of fixed point theory, convex and set-valued analysis,
variational inequality and complementarity problem theory,
non-linear ergodic theory, difference, differential and integral
equations, control and optimisation theory, dynamic system theory,
inequality theory, stochastic analysis and probability theory, and
their applications.
The aim of this volume is to introduce and exchange recent new
topics on the areas of inequality theory and their applications
dealing in pure and applied mathematics.
This is the first in a series of research monographs that focus on
the research, development and use of inequalities in probability
and statistics. All of the papers have been peer refereed and this
first edition covers a range of topics that include both survey
material of published work as well as new results appearing in
print for the first time.
This book provides a primer in inequalities in applied probability
theory & statistics. It is intended to be useful to both
graduate students and established researchers working in
Probability Theory & Statistics, Analytic Integral Inequalities
and their applications in demography, economics, physics, biology
and other scientific areas. The book is self-contained in the sense
that the reader needs only to be familiar with basic real analysis,
integration theory and probability theory. All inequalities used in
the text are explicitly stated and appropriately referenced.
This collection of 12 surveys of previous published works and new
results relate to elements of special function theory. Topics
include special functions approximations and bounds though integral
representation, inequalities for positive Dirichlet series, the
monotonicity of the mean value function of normalized Bessel
functions of the first kind, the application of Sturm Theory for
some classes of Sturm-Liouville equations and inequalities (and the
monotonicity properties for the zeros of Bessel functions,
inequalities for the gamma function through convexity, inequalities
for hyperharmonic series, Hermite-Hadamard inequalities for double
Dirichlet averages and their applications to special functions, new
inequalities involving convex functions, growth rates in Weierstrab
invariants, certain special functions of number theory and
mathematical analysis, an operator related to the Bessel-wave
equation and Laplacian Bessel, and inequalities for Walsh
polynomials with semi-monotone coefficients of higher order.
This research monograph, deals with identities and inequalities
relating to series and their application. This is the first volume
of research monographs on advances in inequalities for series. All
of the papers in this volume have been fully peer reviewed. Some
papers in this volume appear in print for the first time, detailing
many technical results and some other papers offer a review of a
number of recently published results. The papers appear in author
alphabetical order and not in mathematics subject classification.
There are fifteen diverse papers in this volume each with its own
speciality. An important issue in many applications of Probability
Theory is finding an approximate measure of distance, or
discrimination, between two probability distributions. A number of
divergence measures for this purpose have been proposed.
The aim of this volume is to introduce and exchange recent new
topics on the areas of inequality theory and their applications
dealing in pure and applied mathematics.
The purpose of this book is to give a comprehensive introduction to
several inequalities in Inner Product Spaces that have important
applications in various topics of Contemporary Mathematics such as:
Linear Operators Theory, Partial Differential Equations, Non-linear
Analysis, Approximation Theory, Optimisation Theory, Numerical
Analysis, Probability Theory, Statistics and other fields.
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