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Normed Linear Spaces and Banach Spaces
14 other sections not shown
addition and scalar applications approximate solution arbitrary Banach space boundary value problem bounded linear functional bounded linear operator called Cauchy sequence chapter coefficients compact completely continuous computational consider defined denote discussed eigenvalue elements example Exercise exists finite difference methods finite dimensional follows Frechet derivative free surface function spaces functional analysis given Hilbert space implies inequality initial shape initial value problem inner product space integral equation integral operator interval arithmetic interval integral interval valued function iterative method linear operator equations Mathematics matrix metric space Newton iterates Newton's method nonlinear operator equations normed linear space obtain one-one open set orthonormal basis orthonormal sequence partial ordering polynomials rational numbers real line real numbers real valued functions satisfies separable Hilbert space Show space H subspace Suppose surface tension theory topological space two-point boundary value types of convergence unique solution vector zero