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Avkhadiev, Farit Gabidinovich

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Total publications: 77
Scientific articles: 76
Presentations: 3

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Full texts:5632
References:2273
Avkhadiev, Farit Gabidinovich
Professor
Doctor of physico-mathematical sciences (1990)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 20.08.1947
E-mail:
Website: http://kpfu.ru/Farit.Avhadiev
Keywords: conformal mappings, univalent functions, hyperbolic metric, boundary-value problems, isperimetric inequalities, integral inequalities.
UDC: 517.5, 517.54, 517.544, 517.546, 517.956.225, 517.956, 532.5, 517.548, 517.518.28
MSC: 30F10, 30C55, 30C60

Subject:

Geometric Function Theory. Boundary-value problems for analytic functions. Isoperimetric Inequalities of Mathematical Physics.

   
Main publications:
  1. Avkhadiev F.G., Aksentev L.A., “Osnovnye rezultaty v dostatochnykh usloviyakh odnolistnosti analiticheskikh funktsii”, UMN, 30:4(184) (1975), 3–60  mathnet  mathscinet  zmath
  2. Avkhadiev F.G., “Reshenie obobschennoi zadachi Sen-Venana”, Matem. sbornik, 189:12 (1998), 3–12  mathnet  crossref  mathscinet  zmath
  3. Avkhadiev F.G. and Wirths K.-J., Schwarz-Pick Type Inequalities, Birkhäuser, Basel–Boston–Berlin, 2009, 156 pp.  mathscinet
  4. Avkhadiev F.G., “Hardy-Rellich inequalities in domains of the Euclidean space”, J. Math Anal. Appl., 442 (2016), 469-484  crossref  mathscinet
  5. Avkhadiev F.G., Konformno invariantnye neravenstva, Izd-vo Kazanskogo universiteta, Kazan, 2020 https://shelly.kpfu.ru/e-ksu/docs/F940748422/monogr_2020_2.pdf, 260 с.

http://www.mathnet.ru/eng/person8632
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:avkhadiev.farit-gabidinovich
https://mathscinet.ams.org/mathscinet/MRAuthorID/203291
http://elibrary.ru/author_items.asp?spin=5495-2985
http://orcid.org/0000-0001-6927-7102
http://www.researcherid.com/rid/L-4832-2015
http://www.scopus.com/authid/detail.url?authorId=6603621048

Publications in Math-Net.Ru
2020
1. F. G. Avkhadiev, “Properties and applications of the distance functions on open sets of the Euclidean space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, 4,  87–92  mathnet
2019
2. F. G. Avkhadiev, “Conformally invariant inequalities in domains in Euclidean space”, Izv. RAN. Ser. Mat., 83:5 (2019),  3–26  mathnet; Izv. Math., 83:5 (2019), 909–931  isi
3. F. G. Avkhadiev, “On extremal domains for integral inequalities in the Euclidean space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, 6,  80–84  mathnet
4. F. G. Avkhadiev, “One-parameter monotone functionals connected with Stieltjes integrals”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, 4,  3–14  mathnet
5. F. G. Avkhadiev, R. G. Nasibullin, I. K. Shafigullin, “Conformal invariants of hyperbolic planar domains”, Ufimsk. Mat. Zh., 11:2 (2019),  3–18  mathnet; Ufa Math. J., 11:2 (2019), 3–18  isi  scopus
2018
6. F. G. Avkhadiev, “Integral inequalities of Hardy and Rellich in domains satisfying an exterior sphere condition”, Algebra i Analiz, 30:2 (2018),  18–44  mathnet  mathscinet  elib; St. Petersburg Math. J., 30:2 (2019), 161–179  isi  scopus
7. F. G. Avkhadiev, “Brezis–Marcus Problem and Its Generalizations”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 153 (2018),  3–12  mathnet  mathscinet
8. F. G. Avkhadiev, R. G. Nasibullin, I. K. Shafigullin, “$L_p$-versions of one conformally invariant inequality”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, 8,  88–92  mathnet; Russian Math. (Iz. VUZ), 62:8 (2018), 76–79  isi  scopus
9. F. G. Avkhadiev, “On Rellich's inequalities in the Euclidean spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, 8,  83–87  mathnet; Russian Math. (Iz. VUZ), 62:8 (2018), 71–75  isi  scopus
10. F. G. Avkhadiev, “Rellich inequalities for polyharmonic operators in plane domains”, Mat. Sb., 209:3 (2018),  4–33  mathnet  elib; Sb. Math., 209:3 (2018), 292–319  isi  scopus
2017
11. F. G. Avkhadiev, “Conformally invariant inequalities”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 142 (2017),  28–41  mathnet  mathscinet
12. F. G. Avkhadiev, “The generalized Davies problem for polyharmonic operators”, Sibirsk. Mat. Zh., 58:6 (2017),  1205–1217  mathnet  elib; Siberian Math. J., 58:6 (2017), 932–942  isi  scopus
13. F. G. Avkhadiev, “Estimates of Hardy–Rellich constants for polyharmonic operators and their generalizations”, Ufimsk. Mat. Zh., 9:3 (2017),  8–17  mathnet  elib; Ufa Math. J., 9:3 (2017), 8–17  isi  scopus
14. F. G. Avkhadiev, P. L. Shabalin, “Conformal mappings of circular domains on finitely-connected non-Smirnov type domains”, Ufimsk. Mat. Zh., 9:1 (2017),  3–17  mathnet  elib; Ufa Math. J., 9:1 (2017), 3–17  isi  scopus
2016
15. F. G. Avkhadiev, R. G. Nasibullin, I. K. Shafigullin, “Becker type univalence conditions for harmonic mappings”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, 11,  80–85  mathnet; Russian Math. (Iz. VUZ), 60:11 (2016), 69–73  isi  scopus
16. F. G. Avkhadiev, “Rellich type inequalities in domains of the Euclidean space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, 1,  69–73  mathnet; Russian Math. (Iz. VUZ), 60:1 (2016), 60–63  isi  scopus
2015
17. F. G. Avkhadiev, “Sharp constants in Hardy type inequalities”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, 10,  61–65  mathnet; Russian Math. (Iz. VUZ), 59:10 (2015), 53–56  scopus
18. F. G. Avkhadiev, “Hardy type $L_p$-inequalities in $r$-close-to-convex domains”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, 1,  84–88  mathnet; Russian Math. (Iz. VUZ), 59:1 (2015), 71–74  scopus
19. F. G. Avkhadiev, “Integral inequalities in domains of hyperbolic type and their applications”, Mat. Sb., 206:12 (2015),  3–28  mathnet  mathscinet  elib; Sb. Math., 206:12 (2015), 1657–1681  isi  scopus
2014
20. F. G. Avkhadiev, “A geometric description of domains whose Hardy constant is equal to 1/4”, Izv. RAN. Ser. Mat., 78:5 (2014),  3–26  mathnet  mathscinet  zmath  elib; Izv. Math., 78:5 (2014), 855–876  isi  elib  scopus
21. F. G. Avkhadiev, B. S. Timergaliev, “Brunn–Minkowski type inequalities for conformal and Euclidean moments of domains”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, 5,  64–67  mathnet; Russian Math. (Iz. VUZ), 58:5 (2014), 53–56  scopus
22. F. G. Avkhadiev, I. K. Shafigullin, “Sharp estimates of Hardy constants for domains with special boundary properties”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, 2,  69–73  mathnet; Russian Math. (Iz. VUZ), 58:2 (2014), 58–61  scopus
23. F. G. Avkhadiev, R. G. Nasibullin, “Hardy-type inequalities in arbitrary domains with finite inner radius”, Sibirsk. Mat. Zh., 55:2 (2014),  239–250  mathnet  mathscinet; Siberian Math. J., 55:2 (2014), 191–200  isi  scopus
2013
24. F. G. Avkhadiev, “Families of domains with best possible Hardy constant”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, 9,  59–63  mathnet  zmath; Russian Math. (Iz. VUZ), 57:9 (2013), 49–52  scopus
25. F. G. Avkhadiev, I. K. Shafigullin, “Estimates of Hardy's constants for tubular extensions of sets and domains with finite boundary moments”, Mat. Tr., 16:2 (2013),  3–12  mathnet  mathscinet; Siberian Adv. Math., 24:3 (2014), 153–158
2012
26. F. G. Avkhadiev, “Isoperimetric inequality for torsional rigidity in multidimensional domains”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, 7,  45–49  mathnet  mathscinet; Russian Math. (Iz. VUZ), 56:7 (2012), 39–43  scopus
2011
27. F. G. Avkhadiev, “Sharp estimates for functions with a pole and a logarithmic singularity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, 12,  71–75  mathnet  mathscinet; Russian Math. (Iz. VUZ), 55:12 (2011), 58–62  scopus
28. F. G. Avkhadiev, R. G. Nasibullin, I. K. Shafigullin, “Hardy-type inequalities with power and logarithmic weights in domains of the Euclidean space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, 9,  90–94  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 55:9 (2011), 76–79  scopus
2007
29. F. G. Avkhadiev, A. N. Chuprunov, “The probability of a successful allocation of ball groups by boxes”, Lobachevskii J. Math., 25 (2007),  3–7  mathnet  mathscinet  zmath
2006
30. F. G. Avkhadiev, “Hardy type inequalities in higher dimensions with explicit estimate of constants”, Lobachevskii J. Math., 21 (2006),  3–31  mathnet  mathscinet  zmath  elib
31. F. G. Avkhadiev, “Hardy-Type Inequalities on Planar and Spatial Open Sets”, Tr. Mat. Inst. Steklova, 255 (2006),  8–18  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 255 (2006), 2–12  scopus
2005
32. F. G. Avkhadiev, K.-J. Wirths, “Concave schlicht functions with bounded opening angle at infinity”, Lobachevskii J. Math., 17 (2005),  3–10  mathnet  mathscinet  zmath
2004
33. F. G. Avkhadiev, “New isoperimetric inequalities for moments of domains and torsional rigidity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2004, 7,  3–11  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 48:7 (2004), 1–9
2002
34. F. G. Avkhadiev, K.-J. Wirths, “On the coefficient multipliers theorem of Hardy and Littlewood”, Lobachevskii J. Math., 11 (2002),  7–12  mathnet  mathscinet  zmath
35. F. G. Avkhadiev, D. V. Maklakov, “New Equations of Convolution Type Obtained by Replacing the Integral by Its Maximum”, Mat. Zametki, 71:1 (2002),  18–26  mathnet  mathscinet  zmath; Math. Notes, 71:1 (2002), 17–24  isi  scopus
2001
36. F. G. Avkhadiev, R. G. Salahudinov, “Bilateral isoperimetric inequalities for boundary moments of plane domains”, Lobachevskii J. Math., 9 (2001),  3–5  mathnet  mathscinet  zmath
1998
37. F. G. Avkhadiev, “Solution of the generalized Saint Venant problem”, Mat. Sb., 189:12 (1998),  3–12  mathnet  mathscinet  zmath; Sb. Math., 189:12 (1998), 1739–1748  isi  scopus
1997
38. F. G. Avkhadiev, L. A. Aksent'ev, G. G. Bilchenko, “Classes of univalent and multivalent Christoffel-Schwarz integrals and their applications”, Izv. Vyssh. Uchebn. Zaved. Mat., 1997, 3,  64–67  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 41:3 (1997), 63–66
1996
39. F. G. Avkhadiev, A. M. Elizarov, “Sharp estimates for the solution of a variational inverse boundary value problem in a countably connected domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, 3,  3–13  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 40:2 (1996), 1–11
1994
40. F. G. Avkhadiev, S. B. Shabalina, “Zeros of coefficients of transformations and conditions for the solvability of inverse boundary value problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, 8,  3–10  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 38:8 (1994), 1–9
41. F. G. Avkhadiev, D. V. Maklakov, “A criterion for the solvability of the problem of constructing wing profiles based on a cavitation diagram”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, 7,  3–12  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 38:7 (1994), 1–10
42. F. G. Avkhadiev, L. I. Shokleva, “Generalizations of a theorem of Beurling and their applications to inverse boundary value problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, 5,  80–83  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 38:5 (1994), 78–81
1992
43. F. G. Avkhadiev, “The Minkowski functional over ranges of values of the logarithm of the derivative, and univalence conditions”, Trudy Sem. Kraev. Zadacham, 27 (1992),  3–21  mathnet  mathscinet  zmath
1991
44. F. G. Avkhadiev, “Conditions for the univalence of the solution in problems of constructing wing profiles”, Trudy Sem. Kraev. Zadacham, 26 (1991),  3–19  mathnet  mathscinet  zmath
1990
45. F. G. Avkhadiev, “Metrics with variable density, and inverse boundary value problems”, Trudy Sem. Kraev. Zadacham, 25 (1990),  3–23  mathnet  mathscinet  zmath
46. F. G. Avkhadiev, L. A. Aksent'ev, A. M. Elizarov, “Conditions for the univalence of solutions of applied inverse boundary value problems. II”, Trudy Sem. Kraev. Zadacham, 24 (1990),  14–38  mathnet  mathscinet
47. F. G. Avkhadiev, “Univalent solutions of inverse boundary value problems in hydro-aerodynamics”, Trudy Sem. Kraev. Zadacham, 24 (1990),  3–14  mathnet  mathscinet
1989
48. F. G. Avkhadiev, “Estimates in the Zygmund class and their application to boundary value problems”, Dokl. Akad. Nauk SSSR, 307:6 (1989),  1289–1292  mathnet  mathscinet  zmath; Dokl. Math., 40:1 (1990), 217–220
49. F. G. Avkhadiev, “Admissible functionals in injectivity conditions for differentiable mappings of $n$-dimensional domains”, Izv. Vyssh. Uchebn. Zaved. Mat., 1989, 4,  3–12  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 33:4 (1989), 1–12
1987
50. F. G. Avkhadiev, “Injectivity in the domain of open isolated mappings with given boundary properties”, Dokl. Akad. Nauk SSSR, 292:4 (1987),  780–783  mathnet  mathscinet  zmath
51. F. G. Avkhadiev, L. A. Aksent'ev, A. M. Elizarov, “Sufficient conditions for the finite-valence of analytic functions, and their applications”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 25 (1987),  3–121  mathnet  mathscinet  zmath; J. Soviet Math., 49:1 (1990), 715–799
52. F. G. Avkhadiev, L. A. Aksent'ev, A. M. Elizarov, “Conditions for the univalence of solutions of applied inverse boundary value problems. I”, Trudy Sem. Kraev. Zadacham, 23 (1987),  6–24  mathnet  mathscinet
1986
53. F. G. Avkhadiev, L. A. Aksent'ev, “Achievements and problems in sufficient conditions for finite-valence of analytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1986, 10,  3–16  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 30:10 (1986), 1–20
54. F. G. Avkhadiev, S. R. Nasyrov, “Construction of a Riemann surface from its boundary”, Izv. Vyssh. Uchebn. Zaved. Mat., 1986, 5,  3–11  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 30:5 (1986), 1–12
1985
55. F. G. Avkhadiev, S. R. Nasyrov, “Necessary conditions for the existence of a Riemann surface with a given boundary”, Trudy Sem. Kraev. Zadacham, 22 (1985),  6–15  mathnet  mathscinet  zmath
1984
56. F. G. Avkhadiev, “An inverse boundary value problem for a function with singularities”, Trudy Sem. Kraev. Zadacham, 21 (1984),  5–19  mathnet  mathscinet  zmath
1983
57. F. G. Avkhadiev, “Some geometric inequalities and sufficient conditions for $p$-valence”, Izv. Vyssh. Uchebn. Zaved. Mat., 1983, 10,  3–12  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 27:10 (1983), 1–13
58. F. G. Avkhadiev, “Method of locally homeomorphic extension in the theory of sufficient conditions for univalence”, Trudy Sem. Kraev. Zadacham, 20 (1983),  3–10  mathnet  mathscinet  zmath
59. F. G. Avkhadiev, “Univalence of mappings with given properties”, Trudy Sem. Kraev. Zadacham, 19 (1983),  3–14  mathnet  mathscinet  zmath
1976
60. F. G. Avkhadiev, N. B. Salimov, “Univalent solvability of the inverse problem of blast theory”, Trudy Sem. Kraev. Zadacham, 13 (1976),  24–29  mathnet  mathscinet
61. F. G. Avkhadiev, “Singular cases of the principle of correspondence of boundaries”, Trudy Sem. Kraev. Zadacham, 13 (1976),  13–23  mathnet  mathscinet
1975
62. F. G. Avkhadiev, “Sufficient conditions for the univalence of quasiconformal mappings”, Mat. Zametki, 18:6 (1975),  793–802  mathnet  mathscinet  zmath; Math. Notes, 18:6 (1975), 1063–1067
63. F. G. Avkhadiev, L. A. Aksent'ev, “The main results on sufficient cjnditions for an analytic function to be schlicht”, Uspekhi Mat. Nauk, 30:4(184) (1975),  3–60  mathnet  mathscinet  zmath; Russian Math. Surveys, 30:4 (1975), 1–63
1974
64. F. G. Avkhadiev, L. A. Aksent'ev, “Functions of the Bazilevic class in the disc and in an annulus”, Dokl. Akad. Nauk SSSR, 214:2 (1974),  241–244  mathnet  mathscinet  zmath
65. F. G. Avkhadiev, “Some univalent mappings of the half-plane”, Trudy Sem. Kraev. Zadacham, 11 (1974),  3–8  mathnet  mathscinet
1973
66. F. G. Avkhadiev, L. A. Aksent'ev, “The subordination principle in sufficient conditions for univalence”, Dokl. Akad. Nauk SSSR, 211:1 (1973),  19–22  mathnet  mathscinet  zmath
67. F. G. Avkhadiev, “On the weak and the strong problem of univalence in inverse boundary value problems”, Trudy Sem. Kraev. Zadacham, 10 (1973),  3–10  mathnet  mathscinet  zmath
1972
68. F. G. Avkhadiev, “Some sufficient conditions for the univalence of analytic functions”, Trudy Sem. Kraev. Zadacham, 9 (1972),  3–11  mathnet  mathscinet  zmath
1971
69. F. G. Avkhadiev, L. A. Aksent'ev, “Sufficient conditions for univalence of analytic functions”, Dokl. Akad. Nauk SSSR, 198:4 (1971),  743–746  mathnet  mathscinet  zmath
70. F. G. Avkhadiev, “Some sufficient conditions for the univalence of the solutions to applied inverse boundary value problems”, Trudy Sem. Kraev. Zadacham, 8 (1971),  3–11  mathnet  mathscinet  zmath
1970
71. F. G. Avkhadiev, “On sufficient conditions for the univalence of the solutions of inverse boundary value problems”, Dokl. Akad. Nauk SSSR, 190:3 (1970),  495–498  mathnet  mathscinet  zmath
72. F. G. Avkhadiev, “Conditions for the univalence of analytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1970, 11,  3–13  mathnet  mathscinet  zmath
73. L. A. Aksent'ev, F. G. Avkhadiev, “A certain class of univalent functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1970, 10,  12–20  mathnet  mathscinet  zmath
74. F. G. Avkhadiev, “Application of the Schwarzian derivative for the study of the univalent solvability of inverse boundary value problems”, Trudy Sem. Kraev. Zadacham, 7 (1970),  78–80  mathnet  mathscinet  zmath
75. F. G. Avkhadiev, “Radii of convexity and close-to-convexity of certain integral representations”, Mat. Zametki, 7:5 (1970),  581–592  mathnet  mathscinet  zmath; Math. Notes, 7:5 (1970), 350–357
1968
76. F. G. Avkhadiev, V. N. Gaiduk, “An application of close-to-convex functions to inverse boundary value problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1968, 6,  3–10  mathnet  mathscinet  zmath

2014
77. F. G. Avkhadiev, V. A. Botvinnik, S. K. Vodop'yanov, M. Vuorinen, V. M. Gol'dstein, V. V. Goryainov, A. A. Grigor'yan, V. N. Dubinin, I. V. Zhuravlev, V. A. Zorich, V. M. Kesel'man, A. A. Klyachin, V. A. Klyachin, T. G. Latfullin, A. V. Loboda, A. G. Losev, O. Martio, V. I. Pelikh, S. I. Pinchuk, Yu. G. Reshetnyak, A. S. Romanov, A. G. Sergeev, V. G. Tkachev, E. M. Chirka, “Vladimir Mikhailovich Miklyukov (obituary)”, Uspekhi Mat. Nauk, 69:3(417) (2014),  173–176  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 69:3 (2014), 565–568  isi

Presentations in Math-Net.Ru
1. Rellich type inequalities for polyharmonic operators in plane domains
F. G. Avkhadiev
Seminar on Complex Analysis (Gonchar Seminar)
November 14, 2016 17:00
2. Hardy–Rellich type inequalities in domains of the Euclidean space
F. G. Avkhadiev
Seminar on Complex Analysis (Gonchar Seminar)
November 16, 2015 18:00
3. Геометрическое описание областей с максимальными константами Харди
F. G. Avkhadiev
International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii
May 25, 2015 16:40

Organisations
 
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