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Full Description
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.
Contents
A
brief history of the Favard operator and its variants.- Bivariate extension of
linear positive operators.- Positive Green's Functions for Boundary Value
Problems with Conformable Derivatives.- The retraction-displacement condition
in the theory of fixed point equation with a convergent iterative algorithm.- An
adaptive finite element method for solving a free boundary problem with
periodic boundary conditions in lubrication theory.- Evolution solutions of
equilibrium problems - a computational approach.- Cantor, Banach and Baire
theorems in generalized metric spaces.- A Survey of Perturbed Ostrowski Type
Inequalities.- Hyers-Ulam-Rassias stability of the generalized Wilson's
functional equation.- Approximation under Exponential Growth Conditions by Szász
and Baskakov Type Operators in the Complex Plane.- On the asymptotic behavior
of sequences of positive linear approximation operators.- Approximation of
functions by additive and by quadratic mappings.- Bernstein Type Inequalities
concerning Growth of Polynomials.- Approximation for generalization of
Baskakov-Durrmeyer operators.- A Tour on p
(x)-Laplacian Problems When p = ∞.- An umbral calculus approach to
Bernoulli-Padé polynomials.- Hadamard Matrices: Insights into their growth
factor and determinant computations.- Localized summability kernels for Jacobi
expansions.- Quadrature rules with multiple nodes.- A -summability of sequences of linear conservative operators.- Simultaneous
Weighted Approximation with Multivariate Baskakov-Schurer Operators.- Approximation
of Discontinuous Functions by q-Bernstein Polynomials.- Nests, and their Role
in the Orderability Problem.- Resolvent Operators for Some Classes of
Integro-Differential Equations.- Component Matrices of a Square Matrix and
their Properties.- Solutions of Some Types of Differential Equations and of Their
Associated Physical Problems by Means of Inverse Differential Operators.- A
modified pointwise estimate on simultaneous approximation byBernstein
polynomials.- Structural Fixed Point Results in Metric Spaces.- Models of Fuzzy
Linear Regression: An Application in Engineering.- Properties of Functions of
generalized bounded variations.
