Geodesic
Asymptotics of tangent points for planar curves
Matematičeskie trudy, Tome 14 (2011) no. 1, pp. 141-157.

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

In this paper, we prove a universal inequality described the asymptotic behavior of tangent points for differentiable planar curves. As corollaries, we obtain some (partially known) assertions on the asymptotics of mean value points for a number of the classical theorems in analysis. We formulate some unsolved problems. 
@article{MT_2011_14_1_a5,
     author = {Yu. G. Nikonorov},
     title = {Asymptotics of tangent points for planar curves},
     journal = {Matemati\v{c}eskie trudy},
     pages = {141--157},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2011_14_1_a5/}
}
TY  - JOUR
AU  - Yu. G. Nikonorov
TI  - Asymptotics of tangent points for planar curves
JO  - Matematičeskie trudy
PY  - 2011
SP  - 141
EP  - 157
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2011_14_1_a5/
LA  - ru
ID  - MT_2011_14_1_a5
ER  - 
%0 Journal Article
%A Yu. G. Nikonorov
%T Asymptotics of tangent points for planar curves
%J Matematičeskie trudy
%D 2011
%P 141-157
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2011_14_1_a5/
%G ru
%F MT_2011_14_1_a5
Yu. G. Nikonorov. Asymptotics of tangent points for planar curves. Matematičeskie trudy, Tome 14 (2011) no. 1, pp. 141-157. http://geodesic.mathdoc.fr/item/MT_2011_14_1_a5/

[1] Ivanov V. V., Nikonorov Yu. G., “Asimptotika tochek Lagranzha v formule Teilora”, Sib. mat. zhurn., 36:1 (1995), 86–92 | MR | Zbl

[2] Nikonorov Yu. G., “Ob integralnoi teoreme o srednem”, Sib. mat. zhurn., 34:6 (1993), 150–152 | MR | Zbl

[3] Nikonorov Yu. G., “O tochnykh otsenkakh v pervoi teoreme o srednem”, Dokl. RAN, 336:2 (1994), 168–170 | MR | Zbl

[4] Nikonorov Yu. G., Tochnye otsenki v integralnykh teoremakh o srednem znachenii, Dis. $\dots$ kand. fiz.-mat. nauk, IM SO RAN im. S. L. Soboleva, Novosibirsk, 1995

[5] Nikonorov Yu. G., “O resheniyakh nekotorykh integralnykh uravnenii s otklonyayuschimsya argumentom”, Aktualnye problemy sovremennoi matematiki, v. 3, NII MIOO NGU, Novosibirsk, 1997, 136–141 | Zbl

[6] Nikonorov Yu. G., “Otsenki v teoremakh o srednem znachenii dlya operatorov so znakoperemennym yadrom”, Tr. Rubtsovskogo industr. in-ta, 4, 1997, 192–199 | Zbl

[7] Nikonorov Yu. G., “Ob asimptotike tochek srednego znacheniya dlya nekotorykh konechno-raznostnykh operatorov”, Sib. mat. zhurn., 43:3 (2002), 644–651 | MR | Zbl

[8] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, 3-e izd., Nauka, M., 1974 | MR

[9] Riss F., Sekefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979 | MR

[10] Adikesavan A. S., “A note on Taylor's theorem”, Indian J. Pure Appl. Math., 11:4 (1980), 444–449 | MR | Zbl

[11] Jacobson B., “On the mean value theorem for integrals”, Amer. Math. Monthly, 89:5 (1982), 300–301 | DOI | MR | Zbl

[12] Mera R., “On the determination of the intermediate point in Taylor's theorem”, Amer. Math. Monthly, 99:1 (1992), 56–58 | DOI | MR | Zbl

[13] Powers R. C., Riedel T., Sahoo P. K., “Limit properties of differential mean values”, J. Math. Anal. Appl., 227:1 (1998), 216–226 | DOI | MR | Zbl

[14] Sahoo P. K., Riedel T., Mean Value Theorems and Functional Equations, World Scientific Publishing Co., New Jersey, 1998 | MR | Zbl

[15] Trif T., “Asymptotic behavior of intermediate points in certain mean value theorems”, J. Math. Inequal., 2:2 (2008), 151–161 | MR | Zbl

[16] Zhang Bao-lin, “A note on the mean value theorem for integrals”, Amer. Math. Monthly, 104:6 (1997), 561–562 | DOI | MR | Zbl

[17] Xua Aimin, Cuib Feng, Huc Zhicheng, “Asymptotic behavior of intermediate points in the differential mean value theorem of divided differences with repetitions”, J. Math. Anal. Appl., 365:1 (2010), 358–362 | DOI | MR