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| Kazarinoff N. — Analytic inequalities |
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| Предметный указатель |
 -space 77
 -space 77
 35
, series for 45
, Wallis's product for 47 66
Absolute value 7
Ahieser, N.I. 55
Albert, A.A. 1
Apostol, T.M. 1
Archimedes 27
Arithmetic mean 16 17
Arithmetic mean of a function 75
Arithmetic mean, theorem of 17
Berkes, J. 78
Bernstein polynomials 53 54
Bernstein, S.N. 53 55
Besicovitch, A.S. 29
Bing, R.H. 34
Bohr, H. 78
Boltyanskii, V.G. 84
Bunyakovskii, V. 63 71
Cauchy sequence 76
Cauchy's inequality 67 71
Cauchy, A. 63 67 71
CBS-Inequality 72
Cebysev, P.L. 62 78
Complex number 10
Continued fraction 79
Continuity, uniform 56
Convex body or figure 28
Convex function 81
Convex hull 30
Convexity 28
Diameter (set) 84
Duality and dual theorems 26
Dux, E. 80
e, approximation for 40
e, definition of 36
e, irrationality of 62
e, series for 40
Elliptic integral of first kind 51
Erdoes, P. 85
Euclid 15 80
Feller, W. 54
Function, arctan 43
Function, continuous 52 et seq.
Function, convex 81
Function, linear 9
Function, logarithmic 60
Function, monotone 82
Function, sine 50
Function, square root 44 60
Function, uniformly continuous 56
Geometric mean 15—17
Geometric mean of a function 75
Geometric mean, theorem of 17
Greatest lower bound 32
Gregory, James 45
Hardy, G.H. 1 74
Harmonic mean 38 63
Harmonic series 79
Hermite, C. 35
Heron 25
Heron's formula 25
Hilbert space 75 77
Hilbert, David 75
Hoelder's inequality 67
Hoelder's Inequality for complex numbers 71
Hoelder's inequality for integrals 72
Hoelder, O. 63 67
Inequality of geometric and arithmetic means 17 75
Inequality, Cauchy's 67 71
Inequality, CBS 72
Inequality, conditional 6
Inequality, definition of 2
Inequality, determinativeness of 2
Inequality, Hoelder's 67 71 72
Inequality, isoperimetric 27
Inequality, Jensen's 82
Inequality, Minkowski's 69 73
Inequality, triangle 11
Inequality, Wallis's 47 66
Inequality, Young's 82
Infinity, symbol for 48
Isoperimetric problems 15
Isoperimetric theorem for, n-gons 29
Isoperimetric theorem for, quadrilaterals 27
Isoperimetric theorem for, rectangles 17
| Isoperimetric theorem for, right circular cylinders 21 23
Isoperimetric theorem for, tetrahedra 69
Isoperimetric theorem for, triangles 25—26
Isoperimetric Theorem, The 27
Jensen's Inequality (J.L. Jensen) 82
Kakeya, S. 29
Kazarinoff, D.K. 65 85
Kazarinoff, N.D. 84
Lagrange, Joseph Louis 49
Lambek, J. 79
Landau, Edmund 84
Law of Large Numbers 54
Least upper bound 32
Lebesgue integration 76
Lebesgue, Henri 76
Leibnitz, Gottfried Wilhelm 15 45
Lemniscate 13
Lhuilier, Simon 69
Lindemann, F. 35
Littlewood, J.E. 74
ln 2 45 60
Lower bound 31
Mean Value Theorem of Differential Calculus 42
Mean, arithmetic 16 17
Mean, arithmetic of functions 75
Mean, geometric 15—17
Mean, geometric of functions 75
Mean, harmonic 38 63
Mean, power 63 75
Mean, root mean square 63
Minkowski's inequality 69
Minkowski's inequality for integrals 73
Minkowski, Hermann 63 68 71
Moser, J. 79
Nanjundiah, T.S. 62
Newton, Isaac 15 80
Number, 25 45 47 66
Number, algebraic 35
Number, complex 10
Number, e 36
Number, n! 61
Number, prime 80
Number, real 1
Number, transcendental 35
Poisson kernel (Simeon-Denis Poisson, 1781—1840) 83
Polynomials, Bernstein 53
Polynomials, Taylor 52
Power mean 63
Power mean of functions 75
Primes, number of is infinite 80
Primes, sum of reciprocals diverges 80
Real line 1
Real number, absolute value of 7
Real number, order postulates 2
Reflection operation 31
Relative error 39
Right circular cylinder 21 23
Rolle's Theorem (Michel Rolle) 81
Root mean square 63
Schloemilch, O. 64
Schwarz, H.A. 71
Sequence, Cauchy 76
Space, 77
Space,  77
Space, Euclidean 74
Space, Hilbert 75
Space, metric 74
Steiner, Jacob 28
Stirling's formula 61
STIRLING, JAMES 61
Sturm, Rudolph 84
Taylor polynomials 52
Taylor's theorem 49 et seq.
Taylor, B. 48
Theorem of Arithmetic and Geometric Means 17
Theorem of Arithmetic and Geometric Means for functions 75
Triangle inequality 11
Ungar, Peter 85
Uniform continuity 56
Upper bound 31
Wallis's Inequality 47 66
Wallis, John 47 48 65
Weierstrass approximation theorem 52
Weierstrass Approximation Theorem, proof of 55—59
Weierstrass, Karl 27
Weyl, Hermann 76
Yaglon, I.M. 84
Young's Inequality (W.H. Young) 82
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