Mathematical Analysis, Approximation Theory and Their Applications [Hardcover]

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.Abrief history of the Favard operator and its variants.- Bivariate extension oflinear positive operators.- Positive Greens Functions for Boundary ValueProblems with Conformable Derivatives.- The retraction-displacement conditionin the theory of fixed point equation with a convergent iterative algorithm.- Anadaptive finite element method for solving a free boundary problem withperiodic boundary conditions in lubrication theory.- Evolution solutions ofequilibrium problems - a computational approach.- Cantor, Banach and Bairetheorems in generalized metric spaces.- A Survey of Perturbed Ostrowski TypeInequalities.- Hyers-Ulam-Rassias stability of the generalized Wilsonsfunctional equation.- Approximation under Exponential Growth Conditions by Sz?szand Baskakov Type Operators in the Complex Plane.- On the asymptotic behaviorof sequences of positive linear approximation operators.- Approximation offunctions by additive and by quadratic mappings.- Bernstein Type Inequalitiesconcerning Growth of Polynomials.- Approximation for generalization ofBaskakov-Durrmeyer operators.- A Tour on p(x)-Laplacian Problems When p = .- An umbral calculus approach toBernoulli-Pad? polynomials.- Hadamard Matrices: Insights into thel(