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.
