Geodesic
Refinements of integral Cauchy--Bunyakovskii inequality
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 9 (2000), pp. 37-45.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{VSGTU_2000_9_a5,
     author = {S. M. Sitnik},
     title = {Refinements of integral {Cauchy--Bunyakovskii} inequality},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {37--45},
     publisher = {mathdoc},
     number = {9},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2000_9_a5/}
}
TY  - JOUR
AU  - S. M. Sitnik
TI  - Refinements of integral Cauchy--Bunyakovskii inequality
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2000
SP  - 37
EP  - 45
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2000_9_a5/
LA  - ru
ID  - VSGTU_2000_9_a5
ER  - 
%0 Journal Article
%A S. M. Sitnik
%T Refinements of integral Cauchy--Bunyakovskii inequality
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2000
%P 37-45
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2000_9_a5/
%G ru
%F VSGTU_2000_9_a5
S. M. Sitnik. Refinements of integral Cauchy--Bunyakovskii inequality. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 9 (2000), pp. 37-45. http://geodesic.mathdoc.fr/item/VSGTU_2000_9_a5/

[1] Khardi G. G., Littlvud D. E., Polia G., Neravenstva, IL, M., 1948

[2] Bekkenbakh E., Bellman R., Neravenstva, Mir, M., 1965 | MR

[3] Mitrinovic D. S., P. M. Vasic, Analytic inequalities, Springer, 1970 | MR | Zbl

[4] Bullen P. S., Mitrinovic D. S., Vasic P. M., Means and their inequalities, D. Reidel, 1988 | MR | Zbl

[5] Mitrinovic D. S., Pecaric J. E., Fink A. M., Classical and new inequalities in analysis, Kluwer, 1993 | MR

[6] Marshall A., Olkin I., Neravenstva teorii mazhorizatsii i ee prilozheniya, Mir, M., 1983 | MR | Zbl

[7] Bulygin A. M., Koshlakov S. N., Sitnik S. M., “Neravenstva o srednikh v kompleksnoi oblasti”, Nauch.-prakt. konf. VVSh MVD Rossii, Tez. dokl. Chast II, Voronezh, 1998, 6–7

[8] Rado T., “On convex functions”, Trans. Amer. Math. Soc., 37 (1935), 266–285 | DOI | MR

[9] Hartman P., “Convex functions and mean value inequalities”, Duke Math. J., 39:2 (1979), 351–360 | DOI | MR

[10] Sitnik S. M., Teoremy Rado i srednee logarifmicheskoe, Preprint instituta avtomatiki i protsessov upravleniya Dalnevostochnogo otdeleniya RAN, Vladivostok, 1992 | Zbl

[11] Sitnik S. M., Neravenstva dlya srednego logarifmicheskogo i iteratsionnykh srednikh, Preprint instituta avtomatiki i protsessov upravleniya Dalnevostochnogo otdeleniya RAN, Vladivostok, 1992 | Zbl

[12] Stolarsky K. B., “Generalizations of the logarithmic mean”, Math. Mag., 48 (1975), 87–92 | DOI | MR | Zbl

[13] Lin T. P., “The power mean and the logarithmic mean”, AMM, 81 (1974), 879–883 | DOI | MR | Zbl

[14] Carlson B. C., “Some inequalities for hypergeometric functions”, Proc. AMS, 17 (1966), 32–39 | DOI | MR | Zbl

[15] Lupas A., “Problem 12739”, Gaz. Mat., 78:2 (1973), 108

[16] Ostle B., Terwilliger H. L., “A comparison of two means”, Proc. Montana Acad. Sci., 17 (1957), 69–70

[17] Ruthing D., “Eine allgemeine logarithmische Ungleichung”, El. Math., 41 (1986), 14–16

[18] Vserossiiskie matematicheskie olimpiady shkolnikov, Prosveschenie, M., 1992

[19] Pecaric J. E., Dragomir S. S., “A generalization of Hadamard's inequality for isotonic linear functionals”, Radovi Matematicki, 7 (1991), 103–107 | MR | Zbl

[20] Antsiferova G. A., Sitnik S. M., “Nekotorye obobscheniya neravenstva Yunga”, Vestn. Voronezh. i-ta MVD RF, 1999, no. 2(4), 161–164

[21] Borwein J. M., Borwein P. B., Pi and the AGM, Wiley, 1987 | MR | Zbl

[22] Peetre J., “Some observations on algorithms of the Gauss–Borchard type”, Proc. Edinburgh Math. Soc., 34 (1991), 415–431 | DOI | MR | Zbl

[23] Borwein P. B., “Quadratically converging rational mean iterations”, J. Math. Anal. Appl., 154 (1991), 364–376 | DOI | MR | Zbl

[24] Todd J., “The Weierstrass mean”, Numer. Math., 57 (1990), 737–746 | DOI | MR | Zbl

[25] Borwein P. B., “Hypertranscendence of the functional equation”, Proc. AMS, 107 (1989), 215–221 | DOI | MR | Zbl

[26] Loxton J. H., Van der Poorten, “A class of hypertranscendental functions”, Aequationes Math., 16 (1977), 93–106 | DOI | MR | Zbl

[27] Vinogradov I. M., Osnovy teorii chisel, Nauka, M., 1972 | MR

[28] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR

[29] Milne E. A., “Note on Rosseland's integral for the stellar absorption coefficient”, Monthly Notices RAS, 85 (1925), 979–984 | Zbl

[30] Dragomir S. S., Arslanagic S. Z., “A refinements of Cauchy–Buniakowski–Schwarz inequality for real numbers”, Rad. Mat., 7:2 (1991), 299–303 | MR | Zbl

[31] Zigmund A., Trigonometricheskie ryady, T. 1, Mir, M., 1965 ; Т. 2 | MR | Zbl

[32] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[33] Kusis P., Vvedenie v teoriyu prostranstv $H^p$, Mir, M., 1984 | MR

[34] Mitrinovic D. S., Vasic P. M., “History, variations and generalizations of the Cebysev inequality and the question of some priorities”, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 461–497 (1974), 1–30 | MR

[35] Mitrinovic D. S., Pecaric J. E., “History, variations and generalizations of the Cebysev inequality and the question of some priorities, II”, Rad. Jugosl. Akad. Znan. Umj. Mat., 9(450) (1990), 139–156 | MR | Zbl

[36] Beesack P. R., Pecaric J. E., “Integral inequalities of Cebysev type”, J. Math. Anal. Appl., 111:2 (1985), 643–659 | DOI | MR | Zbl

[37] Andreief C., “Note sur relation entre les integrales definies des produits des fonctions”, Brod. Mém., 2(3) (1886), 1–14

[38] Mitrinovic D.S., Pecaric J.E., “Remarks on some determinantal inequalities”, C. R. Math. Rep. Acad. Sci. Canada, 10:1 (1988), 41–45 | MR | Zbl

[39] Sitnik S. M., “Refinements of the Bunyakovskii–Schwartz inequalities with applications to special functions estimates”, Conference in Mathematical Analysis and Applications in Honour of Lars Inge Hedberg's 60 th Birthday (Linkoping University, Sweden. June 10–15), 1996, 97

[40] Sitnik S. M., “Metod polucheniya posledovatelnykh utochnenii neravenstva Koshi–Bunyakovskogo i ego primeneniya k otsenkam spetsialnykh funktsii”, Sovremennye metody v teorii kraevykh zadach, Pontryaginskie chteniya-VII: Tez. dokl., Voronezh, 1996, 164

[41] Sitnik S. M., “Metod polucheniya posledovatelnykh utochnenii neravenstva Koshi–Bunyakovskogo i ego primeneniya k otsenkam spetsialnykh funktsii”, Nauch.-prakt. konf. VVSh MVD Rossii, Tez. dokl. Chast II, Voronezh, 1997, 14

[42] Rodin V. A., “VMO-svoistvo chastichnykh summ ryadov Fure”, DAN SSSR, 319:5 (1991), 1079–1081 | MR | Zbl

[43] Kufner A., Opic B., Hardy-type inequalities, Pitman Research Notes in Mathematics, 219, Longman, Harlow, 1990 | MR | Zbl

[44] Burenkov V. I., Goldman M. L., Obobschennoe neravenstvo Minkovskogo. Neravenstvo Khardi, Izd-vo UDN, M., 1990 | Zbl

[45] Cwikel M., Pustylnik E., “Sobolev type embeddings in the limiting case”, J. Fourier Anal. and Appl., 4:4–5 (1998), 433–446 | DOI | MR | Zbl

[46] Pustylnik E. I., “O nekotorykh svoistvakh vognutykh funktsii samosopryazhennykh operatorov”, DAN SSSR, 186 (1969), 1259–1261 | MR

[47] Pustylnik E. I., “O funktsiyakh pozitivnogo operatora”, Matem. sb., 119(161):1(9) (1982), 32–47 | MR

[48] Pustylnik E., “The rate of convergence of Fourier series with respect to the eigenfunctions of a positive operator”, Funct. Differ. Eq., 4:3–4, 391–403 | MR | Zbl