## Mathematical Analysis, Approximation Theory and Their ApplicationsDesigned 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

2 | |

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 |

### Other editions - View all

Mathematical Analysis, Approximation Theory and Their Applications Themistocles M. Rassias,Vijay Gupta No preview available - 2016 |

### Common terms and phrases

ˆ ˆ ˆ ˇ ˇ ˇ absolutely continuous algorithm Anal Appl Applications approximation properties Approximation Theory asymptotic Banach space Baskakov Bernstein polynomials bivariate bounded variation compact disks complete Comput consider constant continuous functions convergence convex Corollary defined definition denote derivative differential equations Dragomir equivalent exists exponential fixed point formula function f functional equation given Hadamard matrices hence Hermite polynomials Hiſ inequality integral iterative Lemma Let f linear operators Lipschitz mapping Math Mathematical matrix metric space modulus of continuity nonempty obtain orthogonal pivot patterns polynomial of degree problem Proof properties Proposition proved q-Bernstein quadrature rules Rassias result retraction-displacement condition satisfies sequence ſş solution subset TDEP Theorem topology trigonometric polynomials values variable