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Öğe Applications of q-calculus in operator theory(Springer New York, 2013) Aral A.; Gupta V.; Agarwal R.P.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. © Springer Science+Business Media New York 2013. All rights are reserved.Öğe Generalized Szász Durrmeyer operators(2011) Aral A.; Gupta V.In this paper, we introduce and study a new sequence of positive linear operators acting on the spaces of continuous function on positive semi-axis. These operators are defined by means of the q-integral, which generalize the Szász Durrmeyer operators. We study their approximation property by presenting a direct approximation theorem on polynomial weighted spaces and the rate of convergence by means of weighted modulus of continuity. Also, we establish an asymptotic formula with respect to weighted norm. © 2011 Pleiades Publishing, Ltd.
