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Sahoo P.K., Riedel T. — Mean Value Theorems and Functional Equations
Sahoo P.K., Riedel T. — Mean Value Theorems and Functional Equations

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Название: Mean Value Theorems and Functional Equations

Авторы: Sahoo P.K., Riedel T.

Аннотация:

This book takes a comprehensive look at mean value theorems and their connection with functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and the Flett mean value theorems as well as extension to higher dimensions and the complex plane. Furthermore the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 240

Добавлена в каталог: 13.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Aczel, J.      1 7 40 51 57 85 103 109
Alzer, H.      230
Ampere, A.M.      25
Arithmetic-geometric mean, inequality      222
Arithmetic-geometric mean, iteration      222
Aull, C.F.      188 189 192
Aumann, G.      78
Automorphism      18
Bailey, D.P.      51 53 55 56
Banach space      180
Bao-lin, Z.      64 76
Barrett, L.C.      149
Bernoulli’s inequality      31
Bernstein theorem      224
Boggio, T.      83 92
Bonnet, O.      25 214
Borwein, J.M.      228 229
Borwein, P.B.      228 229
Bressoud, D.M.      214
Bruckner, A.      206
Bullen, P.S.      224
Castagnoli, E.      201
Cauchy, A.L.      1 2 77
Central difference quotient      182
Chain rule of differentiation      36
Chung, J.K.      85
Clarke, P.H.      147 159 160
Closed interval      175
Co-ordinate functions      163
Complete elliptic integral      223
Complex conjugate      15 16
Complex numbers system      15
Conjecture      180 230
Continuous extension      60
Convex combination      29
Convex set      157
Courant, R.      127
Critical point      160
Crstici, B.      53
Darboux property      191
Darboux, G.      191
Daroczy, Z.      22 23
Davitt, R.M.      173
Dense in reals      8
Determinant      148
Dieudonne, J.      169
Difference quotient      182
Differentiable function      182
Dini derivatives      195
Divided differences      40
Ebanks, B.R.      22
Eliezer, C.J.      23
Elliptic integral      223
Euclidean inner product      156
Evard, J.C.      147 169 173
Extreme point      164
Flett, T.M.      147 151
Function, additive      1
Function, additive, continuous      2
Function, additive, discontinuous      6
Function, almost open      23
Function, analytic      17
Function, biadditive      18 131
Function, graph      7
Function, holomorphic      169 172 173 177
Function, linear      2
Function, locally increasing      199
Function, locally integrable      3
Function, meaurable      22
Function, multiplicative      12
Function, quadratic      129 135
Function, rationally homogeneous      4
Function, skew-symmetric      22
Functional equation      22 80 85 92 125 127 144 145 230
Functional equation, Cauchy      1 2 50
Functional equation, generalized Jensen      129
Functional equation, Jensen      131
Functional equation, Sincov      97
Fundamental theorem of calculus      31 207
Furi and Martelli’s conjecture      180
Furi, M.      147 149 164 180
Gauss, C.F.      2
Gaussian compound      228
Gaussian mean iteration      228
Generalized binomial coefficient      69
Generalized derivative      181 206
Giorgi, G.      195
Hamel basis      9
Hamel, G.      7
Haruki, H.      230 231
Haruki, Sh.      40 109
Hilbert space      180
Holder inequality      33
Homogeneity      218
Horn, R.A.      28
Horwitz, A.      62 63 81
Hypergeometric differential equation      223
Imaginary part      15
Information theory      32
Integral representation, arithmetic mean      219
Integral representation, generalized means      221
Integral representation, geometric mean      219
Integral representation, identric mean      220
Integral representation, logarithmic mean      38 221
Integral representation, of divided differences      58
Intermediate value property      191
Intermediate Value Theorem      29 61 211 217
Internality      218
Isaacson, E.      58
Iteration of means      207
Jacobian of a function      163
Jacobson, B.      64 69 76
Jacobson, M.S.      43 109 117
Jacobson, R.A.      149
Jafari, F.      147 169 173
Janusz, G.J.      25
Jarai, A.      22 23
Jensen equation      131
Jump discontinuity      186
Kannapan, PL.      43 53 109 117 129 135
Keller, H.B.      58
Komlosi, S.      195
Kranz, L.      225
Kuczma, M.      1 57 83 85 86 91 92 125
Lakshminarasimhan, T.V.      203
Ledyaev, Yu.S.      147 159 160
Legendre, A.M.      2
Liminf      197
Limiting behavior of means      64 69 70
Limsup      197
Line segment      175
Linearly independent      116
Local mean value theorem      177
Maksa, Gy.      22
Marsden, M.      169
Martelli, M.      147 149 164 180
Mays, M.      62
McLeod, R.      147 162
McLeod’s theorem      162
Mean      218
Mean value theorem, a graphical proof      27
Mean value theorem, Cauchy      ix
Mean value theorem, for divided differences, Cauchy      78
Mean value theorem, for divided differences, Lagrange      58 60 69 78
Mean value theorem, for holomorphic functions      169
Mean value theorem, for holomorphic functions, Evard and Jafari      175
Mean value theorem, functions in one variable, Cauchy      77 166
Mean value theorem, functions in one variable, Flett      151 152
Mean value theorem, functions in one variable, Lagrange      25 147
Mean value theorem, functions in one variable, Pompeiu      83
Mean value theorem, functions in one variables, Cauchy      161
Mean value theorem, functions in two variables      163
Mean value theorem, functions in two variables, Cauchy      144
Mean value theorem, functions in two variables, Lagrange      127 156
Mean value theorem, functions in two variables, Pompeiu      145
Mean value theorem, geometrical interpretation      27 30
Mean value theorem, integral      207
Mean value theorem, integral, Bonnet      214
Mean value theorem, integral, Flett      210
Mean value theorem, integral, generalization      208
Mean value theorem, Lagrange      vii
Mean value theorem, nondiffentiable functions, Flett      203
Mean value theorem, nondiffentiable functions, Lagrange      201
Mean value theorem, nondiffentiable functions, Trahan      204
Mean value theorem, of integral calculus      207
Mean value theorem, Pompeiu      viii
Mean value theorem, symmetrically diffentiable functions, Cauchy      194
Mean value theorem, symmetrically diffentiable functions, Flett      193
Mean value theorem, vector valued functions      160
Mean value type equation      129
Mean value type equation, generalization      136
Mean, arithmetic      37 92
Mean, functional      61
Mean, geometric      37
Mean, identric      38
Mean, Lehmer      229
Mean, logarithmic      37
Mean, quasiarithmetic      57
Mean, Stolarsky      36 230
Mitrinovic, D.S.      224
Multidimensional Flett’s theorem      168
Multidimensional Rolle’s theorem      163
Neagu, M.      53
Nested intervals      29
Norm      156
Open ball      164
Open problem      22 80 125 145 228
Optimization problem      181
Ostrowski, A.M.      58
Partial derivative      127 135
Partial derivatives      156
Partition      212
Pompeiu, D.      83
Powers, R.C.      64 70 173
Quadratic polynomial      135 145
Quasi-mean value theorem      190
Rassias, Th.M.      230 231
Rational linear combination      8
Ratz, J.      78
Real part      15
Riedel, T.      64 70 135 173
Riemann sum      212
Rolle’s Theorem      26 166
Rolle’s theorem, for symmetrically diffentiable functions      189
Rouche’s Theorem      177
Russell, D.      78
Sahoo, P.K.      22 43 53 64 70 85 109 117 129 135 173
Samuelsson, A.      147 177
Sander, W.      22
Sanderson, D.E.      147 161
Sayrafiezadeh, M.      212
Schumaker, L.      80
Schwaiger, J.      57
Segment      157 159
Shapiro, H.N.      3
Simpson’s rule      98
Sincov equation      97
Smital, J.      1
Stolarsky, K.B.      62 76
Swann, H.      27
Symmetric derivative      182
Symmetry      218
Taylor’s Formula      72
Taylor’s polynomial      75
Taylor’s Theorem      178
Thews, K.      225
Thomson, B.S.      182
Trahan, D.H.      147 154 158 176 193 204
Tucker, T.W.      28
Uvarov, V.B.      72
Vasic, P.M.      224
Wayment, S.G.      207 210
Wilansky, A.      1
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