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This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of  real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.  .

Mathematics. --- Approximation theory. --- Functional analysis. --- Numerical analysis. --- Approximations and Expansions. --- Numerical Analysis. --- Functional Analysis. --- Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Linear operators. --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems

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Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Mathematics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Operator theory. --- Special functions. --- Computer mathematics. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Operator Theory. --- Special Functions. --- Global Analysis and Analysis on Manifolds. --- Computational Mathematics and Numerical Analysis. --- Mathematical analysis --- Study and teaching. --- 517.1 Mathematical analysis --- Mathematical optimization. --- Functions, special. --- Global analysis. --- Computer science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Special functions --- Functional analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematics --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Isoperimetrical problems --- Variations, Calculus of

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This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several methods are examined to determine moments including direct calculations, recurrence relations, and the application of hypergeometric series. A collection of operators in the theory of approximation are investigated through their moments and a variety of results are surveyed with fundamental theories and recent developments. Detailed examples are included to assist readers understand vital theories and potential applications. .

Mathematics. --- Math --- Science --- Functions of complex variables. --- Differential Equations. --- Differential equations, partial. --- Functional analysis. --- Functions of a Complex Variable. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Complex variables --- Elliptic functions --- Functions of real variables --- Differential equations. --- Partial differential equations.

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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.

Calculus --- Operator theory --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Calculus. --- Integral operators. --- Operators, Integral --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematics. --- Approximation theory. --- Functional analysis. --- Functions of complex variables. --- Approximations and Expansions. --- Functions of a Complex Variable. --- Functional Analysis. --- Integrals --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Theory of approximation --- Functional analysis --- Polynomials --- Chebyshev systems --- Operator theory.

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This book collects original research papers and survey articles presented at the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi Technological University, India, on 23–25 October 2018. Divided into two volumes, it discusses major topics in mathematical analysis and its applications, and demonstrates the versatility and inherent beauty of analysis. It also shows the use of analytical techniques to solve problems and, wherever possible, derive their numerical solutions. This volume addresses major topics, such as operator theory, approximation theory, fixed-point theory, holomorphic functions, summability theory, and analytic functions. It is a valuable resource for students as well as researchers in mathematical sciences.

Operator theory. --- Approximation theory. --- Functional analysis. --- Sequences (Mathematics). --- Operator Theory. --- Approximations and Expansions. --- Functional Analysis. --- Sequences, Series, Summability. --- Mathematical analysis --- 517.1 Mathematical analysis --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems