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Beckenbach E.F., Bellman R. — Inequalities
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Название: InequalitiesАвторы: Beckenbach E.F., Bellman R. Аннотация: Since the classic work on inequalities by Hardy, Littlewood, and Polya in 1934, an enormous amount of effort has been devoted to the sharpening and extension of the classical inequalities, to the discovery of new types of inequalities, and to the application of inqualities in many parts of analysis. As examples, let us cite the fields of ordinary and partial differenlial equations, which aie dominated by inequalities and variational principles involving functions and their derivatives; the many applications of linear inequalities to game theory and mathematical economics, which have triggered a renewed interest in convexity and moment-space theory; and the growing uses of digital computers, which have given impetus to a systematic study of error estimates involving much sophisticated matrix theory and operator theory.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1 editionГод издания: 1961Количество страниц: 198Добавлена в каталог: 14.04.2010Операции: Положить на полку |
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106 107 166—175 Abel, N.H. 32 117 129 Aczel, J. 39 53 Adjoint transformation 79 80 Adjugate matrix 79 80 Aitkin, A.C. 66 90 Alexandroff, P. 80 93 Amir-Moez, A.R. 75 91 Anderson, T.W. 86 96 Andreief, C. 61 88 Arithmetic-geometric mean 10 11 Arithmetic-mean - geometric-mean inequality 3 4 Arithmetic-mean - geometric-mean inequality, refinement of 47 Aronszajn, N. 100 115 129 132 149 165 185 Arrow, K.J. 81 83 84 94 95 159 Artemov, G.A. 146 161 Artin, E. 111 Backward induction 4 5 Banach — Steinhaus theorem 98 118 Banach, S. 94 98 101 107 110 117 118 120 124 125 127 129 139 Beale, E.M.L. 120 Beckenbach's inequality 27 Beckenbach, E.F. 1 16 27 28 50 51 64 89 132 145 146 157 160 Beesack, P.R. 32 53 165 166 178—180 182 185 Bellman, R. 1 2 10 25 30 38 39 48—55 62—67 75—95 105 114—120 126—135 139 141 148 149 154—168 175 182—188 Beltrami, E. 59 132 148 161 Bendat, J. 86 96 Bergman, S. 130 Bergstrom's inequality 67—71 Bergstrom, H. 67—69 71 90 Bernstein's inequality 164 165 Bernstein, S. 109 127 128 164 185 Berwald's inequality 43—44 Berwald, L. 39 43 44 54 101 124 126 Bessel, F.W. 51 99 162 Betti, E. 163 Beurling, A. 55 166 175 186 187 Bieberbach, L. 112 127 Bihari — Langenhop inequality 135 136 Bihari, I. 131 135 136 157 Bing, R.H. 145 160 Birkhoff, G. 31 52 80 82 93 94 Black, H.D. 166 186 Blackwell, D. 52 105 115 126 Blaschke, W. 2 39 53 147 161 177 183 187 Bleuler, K. 146 161 Boas, R.P. 107 127 157 164 165 176 185 187 Bocher, M. 23 51 Bochner, S. 38 53 66 67 100 101 114 124—126 128 148—150 155 157 161—163 Bohnenblust, H.F. 52 80 94 Bohr, H. 1 7 50 Bonnesen, T. 29 50 51 104 105 Bonsall, F.F. 132 145 146 160 Borel, E. 94 101 112 115 120 127 130 159 Borg, G. 166 186 187 Bounded variation 108 Branching process 81 93 94 Brauer, A. 80 86 93 95 Brenner, J.L. 90 Brouwer, L.E.J. 93 Brunacci, V. 32 Brunk — Olkin Inequality 49 Brunk, H.D. 48 49 54 Bueckner, H. 2 39 54 186 Bullen, P. 53 Buniakowsky's inequality 21—23 Buniakowsky, V. 21—23 39 45 47 98 Burgers, J.M. 154 Burton, L.P. 159 Bush, K.A. 64 89 Calabi, E. 157 163 Canonical representation of quadratic form 68 69 Caplygin, S.A. 131 132 139 140 143 146 157 159 161 Caratheodory, C. 103 112—114 119 127 Carlson's inequality 166 175—177 Carlson, F. 166 175 186 Cartan, H. 100 114 125 Carver, W.B. 119 129 Cassels, J.W.S. 45 Caton, W.B. 166 175 186 Cauchy inequality 2 3 60 61 69 70 Cauchy — Buniakowsky — Schwarz inequality 21—23 Cauchy — Buniakowsky — Schwarz inequality, refinement of 45 46 Cauchy — Poincare separation theorem 75 76 Cauchy, A.L. 1 2 18 21 45 50 53 60 69 75 90 91 98 102 104 117 158 161 Cayley, A. 53 Cebyshev, P.L. 97 109 126 127 187 Cernikov, S.N. 119 129 Cesari, L. 118 129 157 Characteristic equation 71 Characteristic root 55 56 68—86 Characteristic root of largest absolute value 80—83 85 Characteristic root of smallest absolute value 85 Characteristic root with largest real part 83 84 Characteristic vector 82 83 Charnes, A. 119 Chassan, J.B. 45 54 Chern, S. 38 53 90 95 Cherry, I. 162 Chevalley, C.C. 131 Coddington, E. 157 163 179 Colautti, M.P. 165 166 180 181 186 Collatz, L. 81 94 156 163 Complete set of inequalities 98 99 102 Completely positive matrix 96 Compound matrix 79 80 Concave function 6 16—19 29 30 39—44 Concave function of a matrix 75 85 Concavity theorem for matrices 62 63 66—68 74 75 Converse inequality 39—45 Convex function 16—19 29 30 48 50 51 84 Convex function of a matrix 85 Convex function, generalized 132 145 146 Convex set 39 99 103—106 108 119 126 Convex space 103 104 Convexo-concave function 18 51 Cooper, J.L.B. 100 114 125 Corduneanu, C. 118 129 Correlation coefficient 50 Cosine, generalized 2 3 50 Courant, R. 73 91 124 165 Cramer, H. 188 Curtis, P.C., Jr. 145 160 Danskin, J.M. 28 51 80 93 Dantzig, G. 119 120 129 Davis, C.S. 61 de Bruijn, N.G. 61 88 Debren, G. 81 94 Decision process 85 Dellac, H. 158 Delsarte, J. 132 147 161 Determinant of a matrix 55 Devinatz, A. 114 128 Diananda, P.H. 50 Differential equation 84 135 144 Differential equation, partial 96 Differential equation, partial, of hyperbolic type 85 Differential inequality 17 18 131—134 168—171 Differential operator 131—134 142—144 164—188 Dines, L.L. 119 129 Dinghas, A. 47 54 Dirichlet, P.G.L. 54 160 Discrete inequality 182—185 Dissipative operator 88 Distance function 28 Dobsch, R. 86 96 Doetsch, G. 157 163 Domain of positivity 56 87 88 Dorfman, R. 81 83 95 101 120 Doubly stochastic matrix 3 Dresher's inequality 28 Dresher, M. 1 28 39 45 51 109 127 du Bois-Reymond, P. 101 126 Dual space 97 Duality 124 125 Duffin, R.J. 86 96 120 130 157 164 Duporeq, E. 158 Dynamic programming 85 95 188 Economy, expanding 83 Eggleston, H.G. 104 126 Ehlers, G. 9 50 Elementary symmetric function 10 11 33—35 78—80 Elliptic equation 148 entropy 55 Erdoes, P. 157 Ergodic theory 55 Esclangon, E. 165 Euclid 23 53 97 103 104 Euler, L. 66 89 124 141 179 Everitt, W.N. 61 88 Expanding economy 83 Fan's inequality 63 74 75 Fan, K. 1 5 32 45 50—56 62 68 71 74—80 84 86 89—96 100 101 110—114 119 120 125—128 166 177 182—186 Farkas, J. 119 129 Favard's inequality 43 44 Favard, J. 39 43 44 54 Fejer, L. 112 113 127 155 Feller, W. 140 159 Fenchel, W. 29 50—52 104 105 Feynman, R.P. 80 92 Fichera, G. 186 Fischer min-max theorem 72 73 Fischer, E. 56 64 72—75 89 91 112—114 127 130 Folges, M. 50 Ford, L.R., Jr. 120 129 Form, quadratic 3 Forsythe, G.E. 123 131 185 188 Forward induction 4 5 Fourier, J.B.J. 15 25 51 97 98 104 113 125 127 128 178 186 187 Frank — Pick inequality 39—44 Frank, P. 39 43 44 53 Fredholm theory 89 Fredholm, I. 89 Friedrichs, K.O. 101 124 126 131 165 185 Frobenius, G. 56 80 93 94 128 Fuchs, L. 31 32 53 Fulkerson, D.R. 120 129 Function of a matrix 75 85 86 Function of a matrix, concave 75 85 Function of a matrix, monotone 86 Function, concave 6 16—19 29 30 39—44 Function, concave, of a matrix 75 85 Function, convex 16—19 29 30 48 50 51 84 Function, convex, generalized 132 145 146 Function, convex, of a matrix 85 Function, convexo-concave 18 51 Function, distance 28 Function, entropy 55 Function, Green's 40—42 93 Function, polar 28 29 Function, positive 99 Function, positive definite 100 114 115 Function, positive real 86 Function, subharmonic 146 Function, superharmonic 146 Functional equation 6 Furstenberg, H. 157 163 Gabriel, R.M. 166 175 186 Gale, D. 119 120 129 130 Games, theory of 7 83 101 120 121 Gantmacher, V. 56 80 87 93 96 Garding's inequality 37 Garding, L. 10 36—38 53 56 66 85 90 95 Garner, J.B. 159 Gass, S.I. 120 130 Gauss, C.F. 10 50 187 188 Gelfand, L. 100 114 Gersgorin's inequality 85 Gersgorin, S. 86 Gerstenhaber, M. 85 95 Glicksberg, I. 25 51 84 91 95 101 120 126 Godemont, R. 100 114 125 Gram, K.P. 51 59 60 88 Gramian 59 60 Graves, L.M. 101 126 Green's function 40—42 93 132—134 141 Green, G. 40 42 93 115 128 129 132 133 141 142 148 149 159 161 Green, J.W. 16 50 156 163 Grenader, U. 100 113 114 128 Greub, W. 45 54 70 Grimshaw, M.E. 76 91 Gronwall, T.H. 131 135 157 158 Gross, O. 25 41 42 51 84 91 95 121 130 Group invariance 67 Guiliano, L. 135 158 Haar — Westphal — Prodi inequality 154 Haar, A. 126 154 162 Hadamard's inequality 64 89 Hadamard, J. 64 89 95 113 158 165 166 185 Hahn, H. 98 101 110 120 124 Halperin, J. 166 172 186 Hamburger, H.L. 76 91 Hardy, G.H. 1 31 32 39 50 51 53 60 129 159 165 166 175 177 179 180 182 186 Harris, T.E. 81 93 94 Hartman, P. 80 93 132 133 144—147 158 160 Hausdorff, F. 128 164 Haviland, E.K. 163 Hayes, W.D. 50 Haynesworth, E.V. 70 86 90 95 Heisenberg, W. 187 Helly, E. 107 110 114 126 Helson, H. 88 97 Herbrand, J. 131 Herglotz, G. 113 114 127 Hermite, C. 53 55—57 64 65 69 85 89—92 119 128 Hermitian matrix 55—57 Hermitian matrix, positive definite 57 64 Hermitian quadratic form 57 Herstein, I.N. 81 94 Hilbert, D. 52 91 98 100 111 114 124 128 165 Hirschman, J.I. 87 96 Hitchcock, H.P. 129 Hoelder's inequality 19—24 Hoelder, O. 1 12 19—21 23 25 27 28 38 39 45 47 51 54 63 98 99 101 104 107 117 167 169 176 Hoffman, A. 62 88 101 120 126 Homogeneity in 21—23 Hopf, E. 163 Hopf, H. 80 93 Hormander, L. 180 188 Horn, A. 75 91 Howard, R. 85 95 Hua, L.K. 65 67 89 Hurwitz, A. 1 8 50 88 117 178 187 Hyers, D. 156 163 Hyperbolic polynomial 36—38 85 90 Hypercomplex number 55 Identity of Lagrange 3 Ince, E.L. 179 187 Induced transformation 79 Induction, backward 4 5 Induction, forward 4 5 Inequality 2 Inequality between arithmetic and geometric means 3 4 Inequality between arithmetic and geometric means, refinement of 47 Inequality for characteristic roots 68—80 Inequality for matrix differential equation 136 137 Inequality for matrix minors 63 64 Inequality for minors of a determinant 63 Inequality for polygons 183 Inequality for squares 2
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