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| Mitrinović D.S., Vasić P.M. — Analytic inequalities |
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| Предметный указатель |
Function, strictly convex 15
Function, strictly J-concave 11
Function, strictly J-convex 11
Function, superadditive 22
Function, symmetric gauge 163
Function, univalent 305
Functions, monotone in the same sense 10
Functions, monotone in the same sense, number-theoretical 366—367
Gabai, H. 344
Gabovic, Ya. (1914) 359
Gabriel's problem 336
Gabriel, R.M. (1902-1957) 336
Gaier, D. (1928) 249
Galvani, L. 16 24
Gamma function 266 285—289
Garnir, H.G. (1921) 235 270 323 325
Gasper, G. (1939) 252 253 254
Gatti, S. 369
Gauss' theorem 165
Gauss, C.F. (1777-1855) V 165 169 300
Gautschi, W. (1927) 179 181 286
Geher, L. (1929) 250 255 350
Gel'man, A.E. (1924) 369
Geometric mean 27 74
Geometric-arithmetic mean inequality 27—29
Geometric-harmonic mean inequality 29
Ger, R. (1945) 15 24
Gerard, F.A. (1907) 294
Gerber, L. 36
Geronimus, Ya.L. (1898) 262
Geysel, J.M. (1940) 125
Ghircoiasiu, N. (1913) 358
Giaccardi, F. (1903-1970) 118
Gibbs, J.W. (1839-1903) 248
Godunova, E.K. (1932) 26 117 118 159 162 279 358 372
Goldberg, K. (1929) 133
Goldman, A.J. (1932) 62 63 64 66
Goldner, F. 198
Goncarov, V.L. (1896-1955) 237 256
Gonkale, D. 287
Goodman, A.W. (1915) 237
Gordon, R.D. (1907) 177 178 180
Gorny, A. 138 140
Gotusso, L. (1936) 25
Gould, H.W. (1928) 361
Gram's determinant 45 46 47 69
Gram's inequality 45—48
Gram's inequality, integral interpretation of 47
Gram's matrix 45
Gram, J.P. (1850-1916) 45 46 47 48 69
Gray, H.L. (1928) 179 180 181
Greenstein, D.S. (1928) 352
Gregory, J. (1638-1675) 188
Greub, W. (1925) 60 65
Grimshaw, M.S. 318
Gronwall's inequality 374
Gronwall, T.H. (1877-1933) 244 246 249 374 375
Gross, W. (1886-1918) 176 177
Gruenwald, T. 231
Gruess' inequality 70—74
Gruess, G. (1902-1950) 64 70 71 72 73 74 191
Gruess, H. (1899) 70
Guha, U.C. (1916) 119 121
Gurland, J. (1917) 286 287
Hadamard's inequality 138
Hadamard, J. (1865-1963) 14 19 23 54 138 139 140 141 152
Hadziivanov, N. (1938) 35 36
Halberstam, H. (1926) 258 259
Halperin, I. (1911) 148 153 176 177
Hamburger, H. (1889-1956) 318
Hamel, G. (1877-1954) 14 23
Hardy's inequality 131
Hardy, G.H. (1877-1947) V VIII IX 19 22 25 30 72 73 78 106 107 118 121 131 138 151 164 167 168 169 170 186 197 226 271 283 299 309
Harmonic mean 27 74
Harmonic-geometric mean inequality 29
Hart, R.G. (1926) 179 181
Hartman, P. (1915) 376 377 378
Hayashi, T. (1873-1935) 40 41 107 108 109 118
Hayman, W.K. (1926) 310 384
Heflinger, L.O. (1927) 361
Henrici's inequality 212 213
Henrici, P. (1923) 61 65 212 213
Hermite, Ch. (1822-1901) 152 212 217
Hermitian 314
Herschorn, M. (1933) 132 137
Herzog, F. (1902) 200
Hilbert space 44 47 59 65 311
Hilbert's inequality 334 357
Hilbert, D. (1862-1943) 44 47 59 65 66 131 287 311 334 357 358
Hill, G.W. (1838-1914) 378
Hille, E. (1894) 260 317 326 358
Hlawka's identity 171
Hlawka's inequality 171—172.
Hlawka's inequality, generalizations of 173—176
Hlawka, E. (1916) 171 172 173 174 176 177
Hochstadt, H. (1925) 378
Hoelder's inequality 43 50—54 64 65 119 356
Hoelder's inequality, integral analogue of 53—54
Hoelder's inequality, inverse of 64—65
Hoelder, O. (1859-1937) 14 23 43 50 51 52 53 54 57 64 65 66 85 103 119 356 380 386
Hoene-Wronski, J.M. (1778-1853) 143
Hofman, J.E. (1900) 194
Holt, J.M. (1930) 160 162
Hornich's inequality 172—173
Hornich, H. (1906) 172 173 176
Hsiang, F.C. (1917) 357
Hsu, N.C. (1927) 221
Hua, L.-K. 157 161 162
Huber, A. (1897) 334
Hughes, I.M. (1927) 372 374
Hukuhara, M. (1905) 21 25
Hummel, P.M. (1908) 185
Hunter, J. 84 85
Hylten-Cavallius, C. (1924) 247 249 251 254 264
Identity of Abel 250
Identity of Binet — Cauchy 42
Identity of Hlawka 171
Identity of Lagrange 41
Increasing function 8
Increasing function, sequence 10
Inequalities in the complex domain 310—336
Inequalities of Carlson 370
Inequalities of Cauchy 204 222
Inequalities of Mathieu 360—361
Inequalities of Popoviciu-type 94 98—102
Inequalities of Rado-type 94 98—102
Inequalities of Redheffer 129—131
Inequalities of Turan 122—125
Inequalities of Wallis 192 287
Inequalities of Weierstrass 210
Inequalities, cyclic 132—138
Inequalities, integral 289—309
Inequalities, involving algebraic functions 198—216
Inequalities, involving derivatives 138—140
Inequalities, involving exponential, logarithmic and gamma functions 266—289
Inequalities, involving functions of discrete variable 187—198
Inequalities, involving means 76—79
Inequalities, involving polynomials 217—235
Inequalities, involving trigonometric functions 235—247
Inequalities, involving trigonometric polynomials 247—265
Inequalities, miscellaneous 336—386
Inequality of Abel 32—33 263
Inequality of Aczel 57
Inequality of Bellman 58
Inequality of Bernoulli 34
Inequality of Bernstein 229
Inequality of Biernacki 116
Inequality of Buniakowski — Schwarz 40 44 71 376
Inequality of Carleman 131
Inequality of Cauchy 30—32 37 41—44 64 77 170 171 207 312 313 314 338 345 379
| Inequality of Cauchy — Schwarz 31
Inequality of Cauchy — Schwarz — Buniakowski 31
Inequality of Cebysev 36—40 64 116 224
Inequality of Diaz — Metcalf 62—64
Inequality of Fan 66—70
Inequality of Fejer — Jackson 255
Inequality of Gram 45—48
Inequality of Gronwall 374
Inequality of Gruess 70—74
Inequality of Hadamard 138
Inequality of Hardy 131
Inequality of Henrici 212 213
Inequality of Hilbert 334 357
Inequality of Hlawka 171—172
Inequality of Hoelder 43 50—54 64 65 103 119 356
Inequality of Hornich 172—173
Inequality of Jensen 109 116 164 236 285
Inequality of Jordan 33
Inequality of Kurepa 58
Inequality of Lagrange 42
Inequality of Lyapunov 54
Inequality of Lyapunov for differential equations 378
Inequality of Markoff 229
Inequality of Minkowski 55—57 356 370
Inequality of Opial 154—162
Inequality of Popoviciu 58
Inequality of Rennie 63
Inequality of Schur 84 119—121
Inequality of Schwarz 44 155 296
Inequality of Schweitzer 59
Inequality of Steffensen 107—119
Inequality of Todd 66—70
Inequality of Weyl 128
Inequality of wirtinger 127 141—154
Inequality of Young 48—50
Ingham, A.E. (1900-1967) 285
Ingleby, C.M. 206
Inner product XII
Intern function 21
Inverse (complementary) inequality of Cauchy's 64
Inverse (complementary) inequality of Cebysev's 64
Inverse inequality of Hoelder'of the triangle inequality 311
Inverse inequality of Hoelder's 64—65
Isayama, S. 40 41
Iyengar, K.S.K. 231 236 297 298 356
Izumi, M. (1930) 258 259
Izumi, S. (1904) 258 259
J-concave function 11
J-convex function 11
J-convex function, continuity of 14—15
Jackson, D. (1888-1946) 248 255 256
Jacobi, K. (1804-1851) 152 253
Janet, M. (1888) VIII 142 143 149 152 154
Janic, R.R. (1931) VIII IX 206
Jensen's inequality 109 164 236 285
Jensen, J.L.W.V. (1859-1925) 10 11 13 14 15 23 25 52 54 109 116 118 164 236 285
Jessen, B. (1907) 285
Jones, G.S. 375
Jordan's inequality 33
Jordan, C. (1838-1922) 33
Jovanovic, S.M. (1935) 240
Kakutani, S. (1911) 317
Kalajdzic, G. (1948) 195 215 269 313 342 343 347 356
Kalinin, V.M. 185
Kantorovic, L.V. (1912) 60 61 65 66 81
Karamata, J. (1902-1967) 73 74 165 169 253 269 272 273 311 312 383 384
Karanicoloff, Chr. (1910) 279
Karlin, S. (1924) 25
Kazarinoff, D.K. (1892-1957) 188 192 193
Kazarinoff, N.D. (1929) 186
Keckic, J.D. (1945) VIII 23 367 368 381
Kelly, L.M. (1914) 176
Kernel, iterated 372 375
Kernel, iterated of Dirichlet 248
Kesava Menon, P. 268 284 289 306
Kesedi, F. 186 191
Kestelman, H. (1908) 94
Khintchine, A. (1894-1959) 194
Kim, W.J. (1937) 145 153
Kingman, J.F.C. (1939) 372 373 374
Kirmser, P.G. (1919) 383
Kirov, G. (1933) 188
Kjellberg, B. (1916) 371
Klamkin, M.S. (1921) 297 385
Kloosterman, H.D. (1900-1968) 324
Kneser, H. (1898) 235
Knopp, K. (1882-1957) 73 74 79 81
Knuth, D.E. (1938) 379
Kober, H. (1889) VII 81 83 85 237 276 322 380
Koksma, J.F. (1904-1964) 258
Kolmogoroff, A.N. see "Kolmogorov A.N."
Kolmogorov, A.N. (1903) 139 140
Komatu, Y. (1914) 178 180 see Y."
Komlos, J. (1942) 125
Konheim, A.G. (1934) 221
Korenbljum, B.I. (1923) 139
Korovkin, P.P. (1913) 186
Kovacs, I. (1933) 250 255 350
Kramer, H. 235
Krasnosel'skii, M.A. (1920) 20 24
Krein, M.G. (1907) 262
Krishnaswami Ayyangar, A.A. 292
Kryzhanovskii, D.A. (1883) 186
Krzyz, J. (1923) 333
Kuczma, M. (1935) 15 24
Kuerschak, J. (1864-1933) 64
Kuhn, H. (1935) 231 384
Kummer, H. 214
Kurepa's inequality 58
Kurepa, S. (1929) VIII 15 24 44 48 57 58 59
Kusmin, R.O. (1891-1949) 258
Kuzmin, R.O. see "Kusmin R.O."
Labutin, D.N. (1902) 37 41
Lackovic, I.B. (1945) 23 368
Lagrange's identity 41
Lagrange's inequality 42
Lagrange, J.L. (1736-1813) 25 41 42 131 275 282 365
Laguerre's polynomial 295
Laguerre, E. (1834-1886) 211 217 295
Lakshmanamurti, M. 347 348
Lambek, J. (1922) 187
Landau, E. (1877-1938) 1 5 72 73 188 191 223 224 258 306 381 382
Langman, H. (1889-1963) 202
Lauffer, R. (1882-1961) 237
Lawrinowicz, J. (1939) 124 125
Lax, P.D. (1926) 228
Lazarevic, I. (1935) 270 321
Lebed', G.K. (1922) 265
Lebesgue, H. (1875-1941) 15 54 116 298 374
Lee, Cheng-Ming (1939) 161 162
Lefort, G. 274
Legendre, A.M. (1752-1833) 152 217
Leibniz, G.W. (1646-1716) 188
Leko, T. (1925) 196
Lemonnier, H. 187
Levi, E.E. (1883-1917) 141 142 149 151 152
Levi, F.W. (1888-1967) 175 177
Levin, A.Yu. (1936) 139 140
Levin, V.I. (1909) VIII 117 118 149 153 159 162 200 358 371 372
Levinson, N. (1912) 155 162 299 309 363 375
Lewin, M. 208 351
Liapounoff, A.M. see "Lyapunov A.M."
Lighthill, M.J. (1924) 132
Liouville, J. (1809-1882) 28 29 30
Littlewood, J.E. (1885) V VIII 22 25 30 78 106 107 118 121 131 138 151 164 167 168 169 170 186 226 299
Ljunggren, W. (1905) 192
Lochs, G. (1907) 270
Logarithmically convex functions 18—20
Lohne, J. 216 219
Lopes, L. (1921) 102 106
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