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A FIRST COURSE IN FUNCTIONAL ANALYSIS
ITERATION AND CONTRACTION MAPPINGS
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Accordingly algebraic apply approximation argument axioms Banach space bounded bounded linear operators calculation Cauchy centre chain chapter Chebyshev polynomials closed ball co-ordinates coefficients condition consider continuous functions contraction operator convergence convex region corresponding curve defined definition of distance derivative differentiation dimensions dual space error Euclidean space example exceed expression fact Figure finite formula Fourier series function f functional analysis geometrical given gives graph Hilbert space idea infinite infinity input instance integral equation interval inverse involved iteration limit linear operator mapping mathematics matrix maximum value means method metric space minimum numerical analysis obtain operator norm origin output perpendicular plane possible problem proof properties prove quadratic question real number result satisfies scalar product sequence solution sphere square subspace suppose supremum symbol tangent tends theorem theory triangle inequality vector space velocity whole number