Isoperimetric inequalities; geometrical theory functions of complex variables; partial differential equations.
Main publications:
Salahudinov R. G. An isoperimetric inequality for torsional rigidity in the complex plane // J. of Inequal. and Appl. 2001. V. 6. P. 253–260.
Avkhadiev F. G., Salahudinov R. G. Bilateral Isoperimetric Inequalities for Boundary Moments of Plane Domains // Lobachevskii J. of Mathematics. 2001. V. 9. P. 3–5.
Avkhadiev F. G., Salahudinov R. G. Isoperimetric Inequalities for Conformal Moments of Plane Domains // J. of Inequal. and Appl. 2002. V. 7(4). P. 593–601.
Avkhadiev F. G., Kayumov I. R., Salakhudinov R. G. Investigations in the theory of functions and isoperimetric problems. (Russian) At the turn of the 20th--21st centuries (Russian), 37–50, Kazan. Mat. Obs., Kazan', 2003.
Salahudinov R. G. Two sided estimations of $L^p$-norms of the warping function of convex domains in $\mathbb R^n$ // Izv. Vuzov. Math. 2006. No 3. P. 41–49. (Russian)
Salahudinov R. G. Estimates of $L^p$-norms of the warping function of plane finite connected domains // Math. zametki. 2006. V. 80, Issue 4. P. 601–613. (Russian)
Salahudinov R. G. Isoperimetric Inequalities for $L^p$-norms of the Distance Function to the boundary // Uchenye Zapiski of Kazan State University. Issue Phys.-Math. sciences. 2006. V. 148, book 2. P. 151–162.
L. I. Gafiyatullina, R. G. Salakhudinov, “A generalization of the Polia–Szego and Makai inequalities for torsional rigidity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 11, 86–91; Russian Math. (Iz. VUZ), 65:11 (2021), 76–80
2019
2.
R. G. Salakhudinov, “Some properties of functionals on level sets”, Ufimsk. Mat. Zh., 11:2 (2019), 118–129; Ufa Math. J., 11:2 (2019), 114–124
2013
3.
R. G. Salakhudinov, “Isoperimetric inequalities for $L^p$-norms of the stress function of a multiply connected plane domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 9, 75–80; Russian Math. (Iz. VUZ), 57:9 (2013), 62–66
R. G. Salakhudinov, “Integral Properties of the Classical Warping Function of a Simply Connected Domain”, Mat. Zametki, 92:3 (2012), 447–458; Math. Notes, 92:3 (2012), 412–421
R. G. Salakhudinov, “Isoperimetric monotony of the $L^p$-norm of the warping function of a plane simply connected domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 8, 59–68; Russian Math. (Iz. VUZ), 54:8 (2010), 48–56
R. G. Salakhudinov, “Two-sided estimates for the $L^p$-norms of the stress function for convex domains in ${\mathbb R}^n$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2006, no. 3, 41–49; Russian Math. (Iz. VUZ), 50:3 (2006), 39–46
R. G. Salakhudinov, “Estimation of the $L_p$-norms of stress functions for finitely connected plane domains”, Mat. Zametki, 80:4 (2006), 601–612; Math. Notes, 80:4 (2006), 567–577
R. G. Salahudinov, “Isoperimetric inequalities for $l^p$-norms of the distance function to the boundary”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 148:2 (2006), 151–162
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