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This book offers advanced graduates and researchers a trove of key results in the study of convergence, in both real and complex domains. It explores new and more efficient applications developed by the authors for studies of optimization and analysis.

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The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new and more efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches.

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1. Preliminaries.- 2. Approximation by Certain Operators.- 3. Complete Asymptotic Expansion.- 4. Linear and Iterative Combinations.- 5. Better Approximation.- 6. Complex Operators in Compact Disks.- 7. Rate of Convergence for Functions of BV.- 8. Convergence for BV/Bounded Functions on Bezier Variants.- 9. Some More Results on Rate of Convergence.- 10. Rate of Convergence in Simultaneous Approximation.- 11. Future Scope and Open Problems.

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From the book reviews:

"Within the field of approximation theory, the book deals with convergence results mainly for linear positive operators, an area of intensive research in the last few decades. It turns out to be a very useful tool for beginners and all those researchers interested in the aforesaid mathematical subject." (Daniel Cárdenas-Morales, zbMATH, Vol. 1295, 2014)
"This monograph should be accessible to anyone familiar with the fundamentals of approximation theory, measure theory and functional analysis. The exposition is essentially self-contained. From this point of view, the book is of great interest to mathematicians and computer scientists working in the field of approximation theory and in related application areas." (Octavian Agratini, Mathematical Reviews, August, 2014)

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