Mathematical Analysis, Approximation Theory and Their Applications

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Themistocles M. Rassias, Vijay Gupta
Springer, Jun 3, 2016 - Mathematics - 741 pages
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.
 

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Contents

A Brief History of the Favard Operator and Its Variants
2
Bivariate Extension of Linear Positive Operators
15
Positive Greens Functions for Boundary Value Problems with Conformable Derivatives
63
The RetractionDisplacement Condition in the Theory of Fixed Point Equation with a Convergent Iterative Algorithm
75
An Adaptive Finite Element Method for Solving a Free Boundary Problem with Periodic Boundary Conditions in Lubrication Theory
107
A Computational Approach
121
Cantor Banach and Baire Theorems in Generalized Metric Spaces
139
A Survey of Perturbed Ostrowski Type Inequalities
145
Insights into Their Growth Factor and Determinant Computations
383
Localized Summability Kernels for Jacobi Expansions
417
Quadrature Rules with Multiple Nodes
435
ASummability of Sequences of Linear Conservative Operators
463
Simultaneous Weighted Approximation with Multivariate BaskakovSchurer Operators
483
Approximation of Discontinuous Functions by qBernstein Polynomials
501
Nests and Their Role in the Orderability Problem
516
Resolvent Operators for Some Classes of IntegroDifferentialEquations
535

HyersUlamRassias Stability of the Generalized Wilsons Functional Equation
218
Approximation Under Exponential Growth Conditions by Szász and Baskakov Type Operators in the Complex Plane
235
On the Asymptotic Behavior of Sequences of Positive Linear Approximation Operators
267
Approximation of Functions by Additive and by Quadratic Mappings
281
Bernstein Type Inequalities Concerning Growth of Polynomials
293
Approximation for Generalization of BaskakovDurrmeyer Operators
317
A Tour on pxLaplacian Problems When p
339
An Umbral Calculus Approach to BernoulliPadé Polynomials
362
Component Matrices of a Square Matrix and Their Properties
559
Solutions of Some Types of Differential Equations and of Their Associated Physical Problems by Means of InverseDifferential Operators
573
A Modified Pointwise Estimate on Simultaneous Approximation by Bernstein Polynomials
630
Structural Fixed Point Results in Metric Spaces
639
An Applicationin Engineering
692
Properties of Functions of Generalized Bounded Variations
714
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