Boundary behaviour of conformal maps, estimates of the integral means spectrum.
Main publications:
H. Hedenmalm, I. Kayumov, “On the Makarov law of the iterated logarithm”, Proceedings of the American Mathematical Society, 135:7 (2007), 2235–2248
I. R. Kayumov, “Lower estimates for integral means of univalent functions”, Arkiv for Matematik, 44:1 (2006), 104–110
И. Р. Каюмов, “Сходимость рядов наипростейших дробей в $L_p(\mathbb R)$”, Матем. сб., 202:10 (2011), 87–98
D. V. Maklakov, I. R. Kayumov, “Exact bounds for lift-to-drag ratios of profiles in the Helmholtz–Kirchhoff flow”, European Journal of Applied Mathematics,, 25:2 (2014), 231–254
I.R. Kayumov, K.-J. Wirths, “Coefficients problems for Bloch functions””, Analysis and Mathematical Physics, 9:3 (2019), 1069–1085
F. G. Avkhadiev, I. R. Kayumov, S. R. Nasyrov, “Extremal problems in geometric function theory”, Russian Math. Surveys, 78:2 (2023), 211–271
2.
A. D. Baranov, I. R. Kayumov, “Estimates for integrals of derivatives of $n$-valent functions and geometric properties of domains”, Sb. Math., 214:12 (2023), 1674–1693
3.
D. V. Maklakov, S. E. Gazizova, I. R. Kayumov, “Optimal velocity distributions in the design of supercavitating hydrofoils”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 8, 71–77
4.
A.D. Baranov, I.R. Kayumov, D.M. Khammatova, R.Sh. Khasyanov, “Weissler and Bernoulli type inequalities in Bergman spaces”, Archiv der Mathematik, 121 (2023), 155-169
5.
A. D. Baranov, I. R. Kayumov, “Estimates for the
integrals of derivatives of rational functions in multiply connected
domains in the plane”, Izv. Math., 86:5 (2022), 839–851
6.
A. D. Baranov, I. R. Kayumov, “Dolzhenko's inequality for $n$-valent functions: from smooth to fractal boundaries”, Russian Math. Surveys, 77:6 (2022), 1152–1154
7.
A. D. Baranov, I. R. Kayumov, “Integral estimates of derivatives of rational functions in Hölder domains”, Dokl. Math., 106:3 (2022), 416–422
8.
I. R. Kayumov, D, M. Khammatova, S. Ponnusamy, “The Bohr Inequality for the Generalized Cesaro Averaging Operators”, Mediterranean Journal of Mathematics, 19:1 (2022), 19 , 16 pp.
A. D. Baranov, I. R. Kayumov, S. R. Nasyrov, “On Bloch seminorm of finite Blaschke products in the unit disk”, Journal of Mathematical Analysis and Applications, 509:2 (2022), 125983 , 10 pp.
I. R. Kayumov, D, M. Khammatova, S. Ponnusamy, “Bohr-Rogosinski phenomenon for analytic functions and Cesaro operators”, Journal of Mathematical Analysis and Applications, 486:2 (2021), 124824 , 17 pp.
I. R. Kayumov, D, M. Khammatova, K.-J. Wirths, “On Landau’s Type Estimates for Coefficients of Univalent Functions”, Computational Methods and Function Theory, 20 (2020), 511-521
14.
I. R. Kayumov, D, M. Khammatova, S. Ponnusamy, “On the Bohr inequality for the Cesaro operator”, Comptes Rendus. Mathématique, 358:5 (2020), 615-620
D. V. Maklakov, I. R. Kayumov, “Stratified laminar flows in inclined pipes”, Russian Math. (Iz. VUZ), 63:11 (2019), 77–82
17.
I. R. Kayumov, “Comparison theorems for certain classes of univalent functions”, BULLETIN of the L.N. Gumilyov Eurasian National University. MATHEMATICS.COMPUTER SCIENCE. MECHANICS Series, 128:3 (2019), 46–52
18.
I.R. Kayumov, K.-J. Wirths, “Coefficient Inequalities for Bloch Functions”, Lobachevskii Journal of Mathematics, 40:9 (2019), 1319–1323
I.R. Kayumov, K.-J. Wirths, “Analogues to Landau's Inequality for Nonvanishing Bounded Functions and for Bloch Functions”, Bulletin of the Malaysian Mathematical Sciences Society, 42:4 (2019), 1737–1744
A. Hinkkanen, I.R. Kayumov, D.M. Khammatova, “Dual Smale's mean value conjecture”, Proceedings of the American Mathematical Society, 147:12 (2019), 5227–5237
S.A. Alkhaleefah, I.R. Kayumov, S. Ponnusamy, “On the Bohr inequality with a fixed zero coefficient”, Proceedings of the American Mathematical Society, 147:12 (2019), 5263–5274
D.V. Maklakov, I.R.Kayumov, R.R.Kamaletdinov, “Stratified laminar flows in a circular pipe: New analytical solutions in terms of elementary functions”, Applied Mathematical Modelling, 59 (2018), 147-163
A. A. Ismagilov, A. V. Kayumova, I. R. Kayumov, S. Ponnusamy, “Bohr Inequalities in Some Classes of Analytic Functions”, J. Math. Sci. (N. Y.), 252:3 (2021), 360–373
29.
I.R. Kayumov, S. Ponnusamy, “Bohr's inequalities for the analytic functions with lacunary series and harmonic functions”, Journal of Mathematical Analysis and Applications, 465:2 (2018), 857–871
I.R. Kayumov, S. Ponnusamy, L.A. Xuan, “On the Analytic Part of Univalent Harmonic Mappings”, Complex Analysis and Operator Theory, 12:5 (2018), 1291–1301
32.
A. Kayumova, I.R. Kayumov, S. Ponnusamy, “Bohr's inequality for harmonic mappings and beyond”, Communications in Computer and Information Science, 834 (2018), 245–256
A. R. Kacimov, D. V. Maklakov, I. R. Kayumov, A. Al-Futaisi, “Free Surface Flow in a Microfluidic Corner and in an Unconfined Aquifer with Accretion: The Signorini and Saint-Venant Analytical Techniques Revisited”, Transport in Porous Media, 116:1 (2017), 115–142
A.A.Afonina, I.R. Kayumov, A.N. Chuprunov, “Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells”, DISCRETE MATHEMATICS AND APPLICATIONS, 2017, no. 5, 277-286
39.
A. I. Afonina, I. R. Kayumov, A. N. Chuprunov, “On the probability of the event: in $n$ generalized allocation schemes the volume of each cell does not exceed $r$”, Ufa Math. Journal, 8:2 (2016), 14–21
40.
A. R. Kacimov, I. R. Kayumov, A. Al-Maktoumi, “Rainfall induced groundwater mound in wedge-shaped promontories: The Strack-Chernyshov model revisited”, Advances in Water Resources, 97 (2016), 110–119
I. R. Kayumov, D. V. Maklakov, “On minimization of cavitational resistance of hydroprofile”, Russian Math. (Iz. VUZ), 59:11 (2015), 68–73
42.
I. R. Kayumov, “A survey on the integral means spectrum for conformal mappings”, Physics and mathematics, v. 157, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, no. 2, Kazan University, Kazan, 2015, 104–115
43.
I. R. Kayumov, D. V. Maklakov, F. D. Kayumov, “Estimates of a spectrum of the integral means for lacunary series”, Russian Math. (Iz. VUZ), 58:10 (2014), 67–72
44.
I. R. Kayumov, “On the Convergence of Series in Spaces of Integrable Functions”, Math. Notes, 95:6 (2014), 780–785
45.
D. V. Maklakov, I. R. Kayumov, “Exact bounds for lift-to-drag ratios of profiles in the Helmholtz–Kirchhoff flow”, European Journal of Applied Mathematics,, 25:2 (2014), 231–254
I. R. Kayumov, A. N. Chuprunov, “The probability of successful allocation of particles in cells (the general case)”, J. Math. Sci., 209:1 (2015), 88–95
47.
I. R. Kayumov, A. V. Kayumova, “Convergence of the imaginary parts of simplest fractions in $L_p(\mathbb R)$ for $p<1$”, J. Math. Sci. (N. Y.), 202:4 (2014), 553–559
48.
D. V. Maklakov, I. R. Kayumov, “One nonlinear variational problem of the theory of cavitating profiles”, Russian Math. (Iz. VUZ), 56:12 (2012), 76–81
49.
I. R. Kayumov, “Integral bounds for simple partial fractions”, Russian Math. (Iz. VUZ), 56:4 (2012), 27–37
50.
I. R. Kayumov, “A Necessary Condition for the Convergence of Simple Partial Fractions in $L_p(\mathbb R)$”, Math. Notes, 92:1 (2012), 140–143
51.
I. R. Kayumov, “Convergence of series of simple partial fractions in $L_p(\mathbb R)$”, Sb. Math., 202:10 (2011), 1493–1504
52.
I. R. Kayumov, “On Holomorphic Motions of $n$-Symmetric Functions”, Math. Notes, 87:6 (2010), 828–833
53.
A. Hinkkanen, I. Kayumov, “Smales problem for critical points on certain two rays”, Journal of the Australian Mathematical Society, 88:2 (2010), 183–191
I. R. Kayumov, “Boundary Behavior of Analytic Riesz Products in the Disk”, Mat. Tr., 9:1 (2006), 34–51
59.
I. R. Kayumov, “On the Law of the Iterated Logarithm for Conformal Mappings”, Math. Notes, 79:1 (2006), 139–142
60.
I. R. Kayumov, “The integral means spectrum and the law of the iterated logarithm for conformal mappings”, Physics and mathematics, v. 148, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, no. 2, Kazan University, Kazan, 2006, 85–96
61.
I. R. Kayumov, “Lower estimates for integral means of univalent functions”, Arkiv for Matematik, 44:1 (2006), 104–110
I. R. Kayumov, “Spectrum of integral means and the modified Bessel function of zero order”, St. Petersburg Math. J., 17:3 (2006), 453–463
63.
I. R. Kayumov, “On Brennan's Conjecture for a Special Class of Functions”, Math. Notes, 78:4 (2005), 498–502
64.
I. R. Kayumov, Yu. V. Obnosov, “Estimates for integral means of hyperbolically convex functions”, Siberian Math. J., 46:6 (2005), 1062–1068
65.
I. R. Kayumov, “Sharp Estimates for Integral Means for Three Classes of Domains”, Math. Notes, 76:4 (2004), 472–477
66.
F. G. Avhadiev, I. R. Kayumov, “Comparison theorems of isoperimetric type for moments of compact sets”, Collect. Math., 55:1 (2004), 1–9
67.
I. R. Kayumov, “A distortion theorem for univalent gap series”, Siberian Math. J., 44:6 (2003), 997–1002
68.
I. R. Kayumov, “The law of the iterated logarithm for locally univalent functions”, Annales Academiae Scientiarum Fennicae Mathematica, 27:2 (2002), 357–364
69.
A. R. Kacimov, I. R. Kayumov, “Viscous flow through straight pore channels”, Journal of Porous Media, 5:3 (2002), 199–208
70.
I. Kayumov, “Lower estimate for the integral means spectrum for p = -1”, Proceedings of the American Mathematical Society, 130:4 (2002), 1005–1007
I. R. Kayumov, “On an extremal problem in airfoil theory”, Russian Math. (Iz. VUZ), 42:11 (1998), 39–44
75.
G. G. Bilchenko, I. R. Kayumov, S. R. Nasyrov, M. F. Sadykov, “Ramified coverings of nonorientable surfaces by orientable surfaces with prescribed boundary projection”, Math. Notes, 63:2 (1998), 253–255
76.
I. R. Kayumov, “Generalization and application of a theorem of Radon”, Russian Math. (Iz. VUZ), 40:4 (1996), 33–36
77.
I. R. Kayumov, V. V. Starkov, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 1996, no. 3, 54–61
78.
F. G. Avkhadiev, I. R. Kayumov, “Estimates in the Bloch class and their generalizations”, Doklady Mathematics, 54:1 (1996), 574–576
79.
F. G. Avhadiev, I. R. Kayumov, “Estimates for Bloch functions and their generalization”, Complex Variables Theory Appl., 29:3 (1996), 193–201
L. A. Aksent'ev, A. I. Aptekarev, A. M. Bikchentaev, V. V. Goryainov, V. N. Dubinin, A. M. Elizarov, I. R. Kayumov, A. Laptev, S. R. Nasyrov, D. V. Prokhorov, A. G. Sergeev, V. D. Stepanov, “Farit Gabidinovich Avkhadiev (on his 70th birthday)”, Russian Math. Surveys, 73:1 (2018), 181–185
О кавитирующих гидропрофилях оптимальной формы I. R. Kayumov, D. V. Maklakov, S. E. Gazizova All-Russian conference "Modern Problems of Continuum Mechanics" devoted to 110 anniversary of L. I. Sedov November 13, 2017 17:05