Mathematical Analysis, Approximation Theory and Their Applications

✍ Scribed by Themistocles M. Rassias, Vijay Gupta (eds.)

• Publisher: Springer
• Year: 2016
• Tongue: English
• Leaves: 745
• Series: Springer Optimization and Its Applications 111
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Front Matter....Pages i-xiv
A Brief History of the Favard Operator and Its Variants....Pages 1-13
Bivariate Extension of Linear Positive Operators....Pages 15-62
Positive Green’s Functions for Boundary Value Problems with Conformable Derivatives....Pages 63-74
The Retraction-Displacement Condition in the Theory of Fixed Point Equation with a Convergent Iterative Algorithm....Pages 75-106
An Adaptive Finite Element Method for Solving a Free Boundary Problem with Periodic Boundary Conditions in Lubrication Theory....Pages 107-120
Evolution Solutions of Equilibrium Problems: A Computational Approach....Pages 121-138
Cantor, Banach and Baire Theorems in Generalized Metric Spaces....Pages 139-144
A Survey of Perturbed Ostrowski Type Inequalities....Pages 145-217
Hyers–Ulam–Rassias Stability of the Generalized Wilson’s Functional Equation....Pages 219-233
Approximation Under Exponential Growth Conditions by Szász and Baskakov Type Operators in the Complex Plane....Pages 235-266
On the Asymptotic Behavior of Sequences of Positive Linear Approximation Operators....Pages 267-280
Approximation of Functions by Additive and by Quadratic Mappings....Pages 281-292
Bernstein Type Inequalities Concerning Growth of Polynomials....Pages 293-316
Approximation for Generalization of Baskakov–Durrmeyer Operators....Pages 317-338
A Tour on p(x)-Laplacian Problems When p = ∞....Pages 339-361
An Umbral Calculus Approach to Bernoulli–Padé Polynomials....Pages 363-382
Hadamard Matrices: Insights into Their Growth Factor and Determinant Computations....Pages 383-415
Localized Summability Kernels for Jacobi Expansions....Pages 417-434
Quadrature Rules with Multiple Nodes....Pages 435-462
Simultaneous Weighted Approximation with Multivariate Baskakov–Schurer Operators....Pages 463-482
Approximation of Discontinuous Functions by q-Bernstein Polynomials....Pages 483-500
Nests, and Their Role in the Orderability Problem....Pages 501-515
Resolvent Operators for Some Classes of Integro-Differential Equations....Pages 517-533
Component Matrices of a Square Matrix and Their Properties....Pages 535-558
Solutions of Some Types of Differential Equations and of Their Associated Physical Problems by Means of Inverse Differential Operators....Pages 559-572
A Modified Pointwise Estimate on Simultaneous Approximation by Bernstein Polynomials....Pages 573-629
Structural Fixed Point Results in Metric Spaces....Pages 631-637
Models of Fuzzy Linear Regression: An Application in Engineering....Pages 639-691
Properties of Functions of Generalized Bounded Variations....Pages 693-713
....Pages 715-741

✦ Subjects

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