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The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.

Integral equations. --- Integral Equations. --- Equations, Integral --- Functional equations --- Functional analysis --- Approximation theory. --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- Teoria de l'aproximació --- Anàlisi funcional --- Funcions --- Polinomis --- Anàlisi numèrica --- Aproximació diofàntica --- Aproximació estocàstica --- Aproximants de Padé --- Interpolació (Matemàtica) --- Pertorbació (Matemàtica) --- Sistemes de Txebixov --- Integral equations --- Numerical solutions. --- Numerical analysis

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Teoria de l'aproximació --- Matemàtica per a enginyers --- Anàlisi matemàtica --- Matemàtica en l'electrònica --- Mecànica aplicada --- Anàlisi dimensional --- Anàlisi funcional --- Funcions --- Polinomis --- Anàlisi numèrica --- Aproximació diofàntica --- Aproximació estocàstica --- Aproximants de Padé --- Interpolació (Matemàtica) --- Pertorbació (Matemàtica) --- Sistemes de Txebixov --- Approximation theory. --- Engineering mathematics. --- Science --- Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Mathematics

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Approximation theory. --- Engineering mathematics. --- Science --- Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Mathematics --- Teoria de l'aproximació --- Matemàtica per a enginyers --- Anàlisi matemàtica --- Matemàtica en l'electrònica --- Mecànica aplicada --- Anàlisi dimensional --- Anàlisi funcional --- Funcions --- Polinomis --- Anàlisi numèrica --- Aproximació diofàntica --- Aproximació estocàstica --- Aproximants de Padé --- Interpolació (Matemàtica) --- Pertorbació (Matemàtica) --- Sistemes de Txebixov

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Operator theory --- Functional analysis --- Numerical approximation theory --- Computer science --- analyse (wiskunde) --- informatica --- wiskunde --- Approximation theory. --- Operator theory. --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- Teoria d'operadors --- Teoria de l'aproximació --- Anàlisi funcional --- Funcions --- Polinomis --- Anàlisi numèrica --- Aproximació diofàntica --- Aproximació estocàstica --- Aproximants de Padé --- Interpolació (Matemàtica) --- Pertorbació (Matemàtica) --- Sistemes de Txebixov --- Teoria dels operadors --- Àlgebres d'operadors --- Equacions d'evolució no lineal --- Operadors diferencials --- Operadors integrals --- Operadors lineals --- Operadors no lineals --- Operadors pseudodiferencials --- Semigrups d'operadors

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This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

Teoria de l'aproximació --- Desigualtats (Matemàtica) --- Processos infinits --- Desigualtats isoperimètriques --- Anàlisi funcional --- Funcions --- Polinomis --- Anàlisi numèrica --- Aproximació diofàntica --- Aproximació estocàstica --- Aproximants de Padé --- Interpolació (Matemàtica) --- Pertorbació (Matemàtica) --- Sistemes de Txebixov --- Desigualtats matricials --- Mathematical optimization. --- Approximation theory. --- Difference equations. --- Functional equations. --- Optimization. --- Approximations and Expansions. --- Difference and Functional Equations. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Equations, Functional --- Functional analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems