Recent Advances in Constructive Approximation Theory

Description

This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators. Front Matter ....Pages i-x Moment Generating Functions and Central Moments (Vijay Gupta, Themistocles M. Rassias, P. N. Agrawal, Ana Maria Acu)....Pages 1-27 Quantitative Estimates (Vijay Gupta, Themistocles M. Rassias, P. N. Agrawal, Ana Maria Acu)....Pages 29-72 Basics of Post-quantum Calculus (Vijay Gupta, Themistocles M. Rassias, P. N. Agrawal, Ana Maria Acu)....Pages 73-89 (p, q)-Integral Operators (Vijay Gupta, Themistocles M. Rassias, P. N. Agrawal, Ana Maria Acu)....Pages 91-133 Univariate Grüss- and Ostrowski-Type Inequalities for Positive Linear Operators (Vijay Gupta, Themistocles M. Rassias, P. N. Agrawal, Ana Maria Acu)....Pages 135-161 Bivariate Grüss-Type Inequalities for Positive Linear Operators (Vijay Gupta, Themistocles M. Rassias, P. N. Agrawal, Ana Maria Acu)....Pages 163-182 Estimates for the Differences of Positive Linear Operators (Vijay Gupta, Themistocles M. Rassias, P. N. Agrawal, Ana Maria Acu)....Pages 183-197 Bivariate Operators of Discrete and Integral Type (Vijay Gupta, Themistocles M. Rassias, P. N. Agrawal, Ana Maria Acu)....Pages 199-240 Convergence of GBS Operators (Vijay Gupta, Themistocles M. Rassias, P. N. Agrawal, Ana Maria Acu)....Pages 241-278 Back Matter ....Pages 279-291