Approximate Solutions to Integral Equations |
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1935 EQUATIONS Alexandria AMERICAN MATHEMATICAL SOCIETY applied approach zero APPROXIMATE SOLUTION Approximating Polynomial arbitrary polynomial assumed assumption auxiliary theorem Bn²n closest coefficients conclusion constant multiple constant not depending continuity not exceeding continuous function convergence theorem denoted discussion dx L(pn E. N. OBERG Reprinted EDWIN NATHANIEL OBERG Enskog EQUATIONS BY E. N. example existence and uniqueness follows Furthermore given function f(x GRADUATE SCHOOL Hence Hölder's inequality hypothesis integral equation L(u interval a≤x≤b involving second derivatives Jackson June kernel Krawtchouk kx(x L(rn least mth power linear Markoff's theorem MATHEMATICAL SOCIETY April maximum McEwen mean value theorem method metodo minimizing minimum modulus of continuity nomial nth degree on(x P₂(x Picone Pn(x Poly polynomial p(x positive constant problem proceed qn(x Reprinted from BULLETIN rn(x SOLUTION OF INTEGRAL square a≤x≤b sufficient condition tion Transactions u-Pn UNIVERSITY OF MINNESOTA upper bound whence