Applications of q-Calculus in Operator Theory [Paperback]

The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such?as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics.?This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using?well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic?definitions of?q-calculus before delving into more advanced material. The?many applications of q-calculus in the theory of approximation, especially on?various?operators,?which includes convergence of operators to functions in real and complex domain forms the gist of the book.

This book is suitable for researchers and?students in mathematics,?physics and?engineering,?and for?professionals who would enjoy exploring the host of mathematical?techniques and ideas that are collected and discussed?in the?book.

This book presents a thorough, systematic introduction to combining approximation theory and q-Calculus with applications, using?well-known operators. At the core of the monograph lie many applications of q-calculus in the theory of approximation.Introduction of q-calculus.- q-Discrete operators and their results.- q-Integral operators.- q-Bernstein type integral operators.- q-Summation-integral operators.- Statistical convergence of q-operators.- q-Complex operators.

From the reviews:

In the book under review, the authors collect up-to-date and important results on the q-type positive linear operators. The book includes many mathematical proof techniques and ideas and it may serve as one of the most useful reference books in this field. Therefore it can be recommended to graduate studel£;