×

zbMATH — the first resource for mathematics

Extended mean values. II. (English) Zbl 0517.26007

MSC:
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26D10 Inequalities involving derivatives and differential and integral operators
26D15 Inequalities for sums, series and integrals
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Askey, R; Gasper, G, Certain rational functions whose power series have positive coefficients, Amer. math. monthly, 79, 327-340, (1972) · Zbl 0242.33023
[2] Carlson, B.C, The logarithmic Mean, Amer. math. monthly, 79, 615-618, (1972) · Zbl 0241.33001
[3] Cisbani, R, Contributi alla teoria delle medie I, Metron, 13, 2, 23-34, (1938) · Zbl 0018.26604
[4] Davenport, H; Pólya, G, On the product of two power series, Canad. J. math., 11, 1-5, (1909) · Zbl 0037.32505
[5] Dunkel, O, Generalized geometric means and algebraic equations, Ann. math., 11, 21-32, (1909) · JFM 40.0124.05
[6] Evans, R, Amer. math. monthly, 79, 1036, (1972), (solution of Problem E 2319)
[7] Galvani, L, Dei limiti a cui tendono alcune media, Boll. un. mat. ital., 6, 173-179, (1927) · JFM 53.0197.02
[8] Garnea, E.G, On a new application of Jacobi polynomials in connection with the Mean value theorem, Bull. amer. math. soc., 49, 541-548, (1943)
[9] {\scC. O. Imoru}, The power mean and the logarithmic mean, Internat. J. Math. Math. Sci., to appear. · Zbl 0483.26012
[10] Kaluza, T, Über die koeffizienten reziproker potenzreihen, Math. Z., 28, 161-170, (1928) · JFM 54.0335.03
[11] Leach, E; Sholander, M, Extended Mean values, Amer. math. monthly, 85, 84-90, (1978) · Zbl 0379.26012
[12] Lin, Tung-Po, The power mean and the logarithmic Mean, Amer. math. monthly, 81, 879-883, (1974) · Zbl 0292.26015
[13] Phillips, G.M, Archimedes the numerical analyst, Amer. math. monthly, 88, 165-169, (1981) · Zbl 0494.65070
[14] Pittenger, A.O, Inequalities between arithmetic and logarithmic means, Univ. beograd. publ. elektrotehn. fak. ser. mat. fiz., 680, 15-18, (1980) · Zbl 0469.26009
[15] Pólya, G; Szegö, G, Isoperimetric inequalities in mathematical physics, (1951), Princeton Univ. Press Princeton, N.J., · Zbl 0044.38301
[16] Stolarsky, K.B, Generalizations of the logarithmic Mean, Math. mag., 48, 87-92, (1975) · Zbl 0302.26003
[17] Stolarsky, K.B, The power and generalized logarithmic means, Amer. math. monthly, 87, 545-548, (1980) · Zbl 0455.26008
[18] Stolarsky, K.B, A stronger logarithmic inequality suggested by the entropy inequality, SIAM J. math. anal., 11, 242-247, (1980) · Zbl 0432.94006
[19] Székely, G, A classification of means, Ann. univ. sci. Budapest. Eötvös sect. math., 18, 129-133, (1975) · Zbl 0336.60004
[20] Tettamanti, K; Sárkány, G; Králik, D; Stomfai, R, Über die annäherung logarithmischer funktionen durch algebraische funktionen, Period. polytech. chem. engrg., 14, 99-111, (1970)
[21] Tobey, M.D, A two-parameter homogeneous Mean value, (), 9-14 · Zbl 0155.10101
[22] {\scD. Zeilberger, J. Gillis and B. Reznick}, On elementary methods in positivity theory, SIAM J. Math. Anal., to appear. · Zbl 0599.42500
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.