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Advances in Summability and Approximation Theory (Hardcover, 1st ed. 2018)
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Advances in Summability and Approximation Theory (Hardcover, 1st ed. 2018)
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This book discusses the Tauberian conditions under which
convergence follows from statistical summability, various linear
positive operators, Urysohn-type nonlinear Bernstein operators and
also presents the use of Banach sequence spaces in the theory of
infinite systems of differential equations. It also includes the
generalization of linear positive operators in post-quantum
calculus, which is one of the currently active areas of research in
approximation theory. Presenting original papers by internationally
recognized authors, the book is of interest to a wide range of
mathematicians whose research areas include summability and
approximation theory. One of the most active areas of research in
summability theory is the concept of statistical convergence, which
is a generalization of the familiar and widely investigated concept
of convergence of real and complex sequences, and it has been used
in Fourier analysis, probability theory, approximation theory and
in other branches of mathematics. The theory of approximation deals
with how functions can best be approximated with simpler functions.
In the study of approximation of functions by linear positive
operators, Bernstein polynomials play a highly significant role due
to their simple and useful structure. And, during the last few
decades, different types of research have been dedicated to
improving the rate of convergence and decreasing the error of
approximation.
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