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
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
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
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, S. Ponnusamy, “The Bohr Inequality for the Generalized Cesaro Averaging Operators”, Mediterranean Journal of Mathematics, 19:1 (2022), 19 , 16 pp.
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
O. V. Ivrii, I. R. Kayumov, “Makarov's principle for the Bloch unit ball”, Sb. Math., 208:3 (2017), 399–412
16.
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, “A Necessary Condition for the Convergence of Simple Partial Fractions in $L_p(\mathbb R)$”, Math. Notes, 92:1 (2012), 140–143
19.
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
21.
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. 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
27.
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. Kayumov, “Smales problem for critical points on certain two rays”, Journal of the Australian Mathematical Society, 88:2 (2010), 183–191
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
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
F. G. Avkhadiev, I. R. Kayumov, “Estimates in the Bloch class and their generalizations”, Doklady Mathematics, 54:1 (1996), 574–576
42.
A. D. Baranov, I. R. Kayumov, “Integral estimates of derivatives of rational functions in Hölder domains”, Dokl. Math., 106:3 (2022), 416–422
43.
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, A. N. Chuprunov, “The probability of successful allocation of particles in cells (the general case)”, J. Math. Sci., 209:1 (2015), 88–95
48.
I. R. Kayumov, “On Holomorphic Motions of $n$-Symmetric Functions”, Math. Notes, 87:6 (2010), 828–833
49.
I. R. Kayumov, “Spectrum of integral means and the modified Bessel function of zero order”, St. Petersburg Math. J., 17:3 (2006), 453–463
50.
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
51.
I. R. Kayumov, K.-J. Wirths, “Inequalities of Carlson Type for $\alpha$ – Bloch Functions”, Mediterranean Journal of Mathematics, 17:3 (2020), 1-9
D. V. Maklakov, I. R. Kayumov, “Stratified laminar flows in inclined pipes”, Russian Math. (Iz. VUZ), 63:11 (2019), 77–82
53.
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
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
55.
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
56.
I. R. Kayumov, “Boundary behavior of the power series of the enlarged Bloch class”, Siberian Math. J., 50:3 (2009), 450–455
57.
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
58.
I. R. Kayumov, “Sharp Estimates for Integral Means for Three Classes of Domains”, Math. Notes, 76:4 (2004), 472–477
59.
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
60.
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
61.
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
62.
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
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
65.
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
66.
I. R. Kayumov, D. V. Maklakov, “On minimization of cavitational resistance of hydroprofile”, Russian Math. (Iz. VUZ), 59:11 (2015), 68–73
67.
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
68.
I. R. Kayumov, “On the Convergence of Series in Spaces of Integrable Functions”, Math. Notes, 95:6 (2014), 780–785
69.
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
70.
I. R. Kayumov, Yu. V. Obnosov, “Estimates for integral means of hyperbolically convex functions”, Siberian Math. J., 46:6 (2005), 1062–1068
71.
F. G. Avhadiev, I. R. Kayumov, “Comparison theorems of isoperimetric type for moments of compact sets”, Collect. Math., 55:1 (2004), 1–9
72.
I. R. Kayumov, “The law of the iterated logarithm for locally univalent functions”, Annales Academiae Scientiarum Fennicae Mathematica, 27:2 (2002), 357–364
73.
A. R. Kacimov, I. R. Kayumov, “Viscous flow through straight pore channels”, Journal of Porous Media, 5:3 (2002), 199–208
74.
I. R. Kayumov, “The integral means spectrum for lacunary series”, Annales Academiae Scientiarum Fennicae Mathematica, 26:2 (2001), 447–453
75.
I. R. Kayumov, “On an extremal problem in airfoil theory”, Russian Math. (Iz. VUZ), 42:11 (1998), 39–44
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.
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
79.
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
80.
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