Peajcariaac J.E., Tong Y.L. — Convex functions, partial orderings, and statistical applications :: Электронная библиотека попечительского совета мехмата МГУ

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Peajcariaac J.E., Tong Y.L. — Convex functions, partial orderings, and statistical applications

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Название: Convex functions, partial orderings, and statistical applications

Авторы: Peajcariaac J.E., Tong Y.L.

Аннотация:

This research-level book presents up-to-date information concerning recent developments in convex functions and partial orderings and some applications in mathematics, statistics, and reliability theory. The book will serve researchers in mathematical and statistical theory and theoretical and applied reliabilists.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 484

Добавлена в каталог: 17.11.2013

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Предметный указатель

Jodeit, M.      63 89 428
Jordan, D.      138 431
Jovanovic, M.      41 431 434
Jurkat, W.B.      289 290 431
Kainuma, D.      52 53 431
Kalusa, Th.      288 431
Kantorovich, L.V.      292 431
Karamanov, V.G.      41 432
Karamata, J.      212 271—273 288 290 320 431 432
Karlin, S.      23 25 26 30 159 161 200 213 254 267 269 298 341 348 355 358 432
Keckic, J.D.      7 8 81 82 130 131 133 175—177 279 432 453
Keilson, J.      364 432
Keller, H.B.      15 431 438
Kendall, M.G.      417 432
Kenyon, H.      7 432
Klamkin, M.S.      134 166—168 432 445
Klee, V.L.      7 432
Knopp's inequality      234
Knopp, K.      102 112 212 432
Kobayashi, K.      218 431
Kober, H.      180 433
Kocic, Lj.M.      40 55 133 134 140 146 258 259 261 265 266 433 435 438 439
Kolmogorov, A.N.      269 433
Korablev, A.I.      41 433
Koskela, M.      135 433
Kosmak, L.      293 433
Kotkowski, B.      281 433
Kovacec, A.      259 269 433
Krafft, N.      218 422 433
Krasnosel'skii, M.A.      241 242 245 433
kth order divided difference      14
kth order divided difference and higher-order convex functions      14
kth order divided difference, integral representation of      15
Kubo, F.      52 53 428 433
Kuczma, M.      4 6 22 23 53 128 433
Kuhn, N.      55 434
Lackovic, I.B.      4 8 55 72 81 82 137 143 147 148 175 204 245 248 258 262 265 277 279 280 281 283 290 292 294 432—434 439 451 453
Lah, P.      98 435
Landau, E.      211 435
Lapidot, E.      30 435
Laplace, P.S.      217 435
Lawrence, S.      72 435
Leach, E.B.      120 435
Lehmann, E.L.      394 400 435
Levin, V.I.      80 188 191 224 225 227 228 235 237 429
Levinson, N.      71 435
Liapunov's inequality for isotonic functionals      117
Lieb, E.H.      353 354 423
Lieberman, G.      411 426
Littlewood, J.E.      1 4 6 45 72 108 139 152 154 165 182 199 234 300 301 303 319 320 361 365 409 430
Liu, W.W.      341 435
Loeve, M.      343 344 435
Log-concave density functions and Prekopa's theorem      294—295 348—351
Log-concave density functions and Schur-concave density functions      355
Log-concave density functions, properties of      353—355
Log-concave functions      7 304—305 348—351
Log-concave functions, closure properties of      294 295 383
Log-concave functions, definition of      7
Log-concave sequences      302
Log-concave sequences, closure properties of      289
Log-convex functions      7 304 305 363 364
Log-convex functions and convex functions      7
Log-convex functions, definition of      7
Log-convex functions, examples of      364
Log-convex sequences      302
Log-convex sequences, closure properties of      284 288 290 294
Lopes, L.      303 436
Lorentz, G.G.      289 325 329 330 411 427 435
Lovera, P.      278 435
Lupas, A.      35 142 143 172 204 208 212 281—283 294 305 435 436
Lupas, L.      210 436
Lusternik, I.      348 436
Macbeath, A.M.      348 430
Magnus, A.      62 436
Majorization and convex functions      319 323 333
Majorization and doubly stochastic matrices      321
Majorization and partial ordering of triangles      307—313
Majorization and Schur's condition      312
Majorization and Schur-concave functions      332
Majorization and Schur-convex functions      332
Majorization for functions      324 325
Majorization, definition of      75 319
Majorization, multivariate majorization and n-dimensional rectangles      358
Majorization, multivariate majorization, definitions of      337
Majorization, submajorization      320—321
Majorization, supermajorization      321
Maksimovic, D.M.      133 134 147 433 436 453
Mansion, P.      138 431
Marcus — Lopes Inequality      303
Marcus, M.      243 303 423 424 436
Marik, J.      272 436
Markovic, D.      82 436
Marshall — Olkin Theorem      335
Marshall — Olkin — Proschan Inequality      155
Marshall — Proschan Inequality      362
Marshall, A.W.      155 156 218 254 294 307 319—321 329 333—335 337 338 340 345 359 361 362 372 380 381 386—388 409 420 437
Matric, B.      33 437
McLaughlin, H.W.      118 437
McLeod, J.B.      303 437
McShane's inequality      48 49 127
McShane, E.J.      48—51 95 240 437
Meir, A.      167 437
Menon, K.V.      289 437
Merkle, M.J.      244 437
Mesihovic, B.A.      105 201 205 256 274 283 437 446
Metcalf, F.T.      118 240 426 437
Micchelli, C.A.      19 20 424 437
Miescke, K.J.      401 402 429
Mijalkovic, Z.M.      88 92 438 453
Mikusinski, J.G.      7 438
Milicevic, M.      244 438
Milisavljevic, B.      39 438
Milovanovic, G.V.      16 35 39 166 167 210 217 225 426 438
Milovanovic, I.Z.      40 53 166 167 210 217 218 225 250 251 255—257 259 260 266 275 283 284 433 438 439 446 450 451 454
Minc's inequalities      412
Minc, H.      412 439
Minkowski inequality      166
Minkowski Inequality for isotonic functionals      114
Minkowski Inequality, generalizations of      127 128
Minkowski, H.      348 439
Mirsky, L.      89 199 322 424 439
Mitrinovic — Pecaric Inequality      90
Mitrinovic, D.S.      39 44 55 71 72 80—82 88 90 95 96 99 104 109 112 115 118 120 124 126—128 131 134 135 137 154 156 159 161 162 166 171 180—182 188 190 195 198—200 203 208 209 211 212 221 222 224 226 231 233 234 244 245 251 254 256 259 262 269 271 274 277 278 290 292 294 295 300 302—304 307 316 317 320 324 325 364 421 424 439 440
Mitrovic, Z.M.      279 453
Mocanu, C.      280 440
Moldovan, E.      293 440
Montel, P.      278 440
Mott, T.E.      278 440
Mueller, M.      305 436
Muirhead's theorem      361
Muirhead's theorem and inequalities for means      365
Muirhead's theorem, generalizations of      361—364
Muirhead's theorem, integral form of      363
Mulholland, H.P.      166 440
Multivariate arrangement decreasing (MAD) functions      412
Multivariate arrangement increasing (MAI) functions      407 411
Multivariate arrangement increasing (MAI) functions and AI functions      414 416
Multivariate arrangement increasing (MAI) functions and Lorentz's inequality      411
Multivariate arrangement increasing (MAI) functions and measures of agreement      417 418
Multivariate arrangement increasing (MAI) functions and Ruderman's inequality      411
Multivariate arrangement increasing (MAI) functions and Schur-convex functions      410
Multivariate arrangement increasing (MAI) functions, definition of      408
Multivariate arrangement increasing (MAI) functions, examples of      410—412 414
Multivariate arrangement increasing (MAI) functions, preservation and closure properties of      413—416
Multivariate majorization      see "Majorization"
Multivariate probability inequalities for distribution functions      335
Multivariate probability inequalities for long-concave probability measures      349—351
Multivariate probability inequalities for n-dimensional rectangles      358
Multivariate probability inequalities, dimension-related      343—347 366—371
Multivariate totally positive of order two ( $MTP_{2}$ ) functions      409

Multivariate totally positive of order two ( $MTP_{2}$ ) functions and multivariate AI functions      410
N-Functions      241 242
N-Functions and Young's inequality      242
Nakamura, M.      51—53 431 440
Nanson's inequality      247
Nanson's inequality, generalizations of      248 250 251
Nanson, E.J.      247 440
Narumi, S.      223 441
Nazarov, I.M.      199 422
Nehari, Z.      224 441
Neuman, E.      21 38 79 149—151 441
Nevius, S.E.      383 441
Newman, D.J.      166—168 432 441
Nieto, J.I.      240 441
Nishiura, T.      217 441
Noerlund, N.E.      23 441
Novikoff, A.      341 432
Ogura, K.      202 441
Olkin, I.      155 218 254 294 307 319—321 329 333—335 337 338 340 345 359 362 372 380 381 386—388 409 437
Olovyanisnikov, V.M.      32 441
One-variable convex functions and compositions of functions      7
One-variable convex functions and continuity      6
One-variable convex functions, closure properties of      5
One-variable convex functions, definition of      1
One-variable convex functions, derivatives of      4 5
Opial's inequality      162 239
Opial, Z.      162 441
Oppenheim, A.      80 246 315 441 442
Ordering of convexity      8 279—281
Ostrow, E.      8 279 424
Ostrowski's inequality      209
Ostrowski, A.M.      195 207 209 210 442
Ozeki, N.      180 277 278 284 286 288—291 302 303 442
Page, E.B.      400 442
Partial ordering of triangles via majorization      307—313
Pavolovic, S.      155 442
Pecaric, J.E.      6 16 21 27 32 35 36 39 45 55 56 57 59 62 63 66—68 70—72 74 76 79 81 83 86 88—90 92 93 96—98 101 103 105 111 117 118 122 124 126 133—135 145 146 148—152 154—157 159 161—163 165—167 171 173 175 180 183 184 188 190 192—194 199 200 204 205 207 209 213 215 217 218 221 222 224—226 232—234 247—251 253—260 262 274 275 278 282—284 292 301 307 316 317 324 325 328 419 422 426 438—446 451 454
Peetre, J.      292 446
Persson, L.E.      292 446
Petrovic's inequality      154 324
Petrovic's inequality, generalizations of      155
Petrovic, M.      130 154 155 446
Petschke, M.      195 446
Picard, E.      138 446
Pick, G.      212 422 428
Pidek, H.      206 422
Pirie, W.R.      400 446
Pitenger, A.O.      142 446
Pollak, M.      367 368 394 448
Pollard, H.      272 426
Ponstein, J.      7 447
Popoviciu's inequality      171
Popoviciu's inequality for isotonic functionals      125
Popoviciu, T.      1 5 16—18 21 23 47 71 89 102 124 154 171 175 199 213 214 259 261 262 293 294 447
Prekopa's theorem      349
Prekopa's theorem and n-dimensional rectangles      358
Prekopa, A.      295 347 349 353 447
Proschan — Sethuraman Theorem      335—336 383
Proschan — Sethuraman — Tong Inequality      364—365
Proschan, F.      155 156 218 295 329 330 334 345 354 361—364 368 373 375 383 387 391 394 397 400 401 405 407 414—416 419 420 422 423 427 430 437 441 447 448
Psenicynyi, B.N.      241 448
Quasi-arithmetic mean      231 300 301
Quasi-convex functions      7 40 41
Quasi-convex functions and quotient of means of nonnegative functions      292
Quasi-convex functions, definition of      7
Quasi-convex functions, strongly quasiconvex functions      40
Quasi-convex functions, weakly quasiconvex functions      42
Rado, T.      141—143 448
Rahmail, R.T.      217 224 225 448
Rasa, I.      4 47 48 97 247 420 448
RibariC, M.      98 435
Riekstyn's, E.Ja.      182 305 448
Rinott, Y.      338 347 351 355 358 367 368 394 448
Ripianu, D.      294 420
Roberts, A.W.      1 4—7 9—13 53 70 141 241 325 448
Rockafellar, R.T.      42 448
Roghi, G.      209 448
Root-increasing functions, closure property of      296
Root-increasing functions, definition of      296
Ross, D.K.      305 411 426 448
Roulier, J.      265 423
Royden, H.L.      299 448
Rozanova, G.I.      235 237—239 448 449
Ruderman's inequality      411
Ruderman, H.D.      411 449
Ruticii, Ya.B.      241 242 245 433
Rutkowski, I.      201 449
Ryff, J.V.      363 449
Ryll-Nardzewski, C.      206 422
Sandor, I.      135 151 427 449
Santner, T.J.      400 449
Savage, I.R.      398 399 449
Savic, B.      27 30 32 274 446 449
Schnitzer, F.      217 441
Schoenberg, I.J.      15 31 32 293 424 447 449
Schur's (Schur — Ostrowski) condition      310 312 333
Schur, I.      310 332 449
Schur-concave functions      310—312 332
Schur-concave functions and majorization      332
Schur-concave functions, definition of      332
Schur-convex functions      75 310—312 332 365
Schur-convex functions and distribution functions      335
Schur-convex functions and higher order convex functions      76
Schur-convex functions and majorization      332
Schur-convex functions and permutation-invariant convex functions      334—334
Schur-convex functions, closure properties of      334—336
Schur-convex functions, definition of      75 332
Second integral mean value theorem      270
Segalman, D.      72 435
Seitz, G.      202 449
Semigroup property      297
Sethuraman, J.      334 363 364 372 375 383 387 397 414 430 441 447 448
Shaked, M.      344 367 394 449
Sharma, B.D.      19 292 424 449
Shisha, O.      77 430
Sholander, M.C.      120 435
Shore, T.R.      135 449
Sidak, Z.      347 449
Sign-changes of a measure      267—269
Simic, S.K.      279 434
Similarly-ordered functions      199
Similarly-ordered functions, definition of      199
Similarly-ordered sequences      199
Similarly-ordered sequences, definition of      199
Sirotkina, A.A.      56 450
Slater's inequality      66—67 69
Slater, M.L.      63 66 450
Sobel, M.      400 405 430
Stankovic, Lj.R.      4 72 73 75 80 159 172 173 199 217 224 225 248 323 424 450
Stankovic, M.S.      39 148 277 281 283 290 292 294 434 438 439
Star-shaped functions      8 296
Star-shaped functions in mean      8
Star-shaped functions, definition of      296
Star-shaped functions, inequalities for      see "Inequalities"
Star-shaped sequences of order m      257
Star-shaped sequences, inequalities for      258
Star-shaped sequences, orderings for      279 281—284
Steffensen's inequality      181
Steffensen's inequality and Jensen — Steffensen Inequality      181
Steffensen's inequality, generalizations of      182 184 192—175
Steffensen, J.F.      57 181 182 187 199 450
Steinig, J.      247 450
Steklov functions      139
Stojanovic, N.M.      256 260 266 283 439 454
Stolarsky, K.B.      119 120 450
Stoyan, D.      341 450
Studden, W.J.      23 25—27 159 161 200 213 254 267 269 432
Subadditive functions      8 176—178 180 280 409
Subadditive functions in mean      8
Subadditive functions, closure property of      300

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