Applications of q-Calculus in Operator Theory [electronic resource] / by Ali Aral, Vijay Gupta, Ravi P Agarwal.
Contributor(s): Gupta, Vijay [author.] | Agarwal, Ravi P [author.] | SpringerLink (Online service)Material type: TextPublisher: New York, NY : Springer New York : Imprint: Springer, 2013Description: XII, 262 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781461469469Subject(s): Mathematics | Approximation theory | Functional analysis | Functions of complex variables | Mathematics | Approximations and Expansions | Functions of a Complex Variable | Functional AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 511.4 LOC classification: QA401-425Online resources: Click here to access online
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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.
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.