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