Ukr. Mat. Zh. - 2017. - 69, № 5. - pp. 582-598
We continue studying on the Nikol’skii and Bernstein –Walsh type estimations for complex algebraic polynomials in the bounded and unbounded quasidisks on the weighted Bergman space.
Ukr. Mat. Zh. - 2014. - 66, № 6. - pp. 826–834
We motivate a new sequence of positive linear operators by means of the Chlodovsky-type Szasz–Mirakyan–Bernstein operators and investigate some approximation properties of these operators in the space of continuous functions defined on the right semiaxis. We also find the order of this approximation by using the modulus of continuity and present the Voronovskaya-type theorem.
Ukr. Mat. Zh. - 2011. - 63, № 9. - pp. 1263-1278
Some new oscillation criteria are established for the nonlinear damped differential equation $$(r(t)k_1 (x, x'))' + p (t) k_2 (x, x') x' + q (t) f (x (t)) = 0,\quad t \geq t_0.$$ The results obtained extend and improve some existing results in the literature.
Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 714–721
The main purpose of this paper is to give sufficient conditions for the convergence of solutions of a certain class of fourth-order nonlinear differential equations using Lyapunov’s second method. Nonlinear functions involved are not necessarily differentiable, but a certain incrementary ratio for a function h lies in a closed subinterval of the Routh–Hurwitz interval.