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Properties of solutions of a heterogeneous differential equation of the second order
(2019) Mulyava, Oksana; Sheremeta, Miroslav; Trukhan, Yu. S.
Suppose that a power seriesA(z) =∑∞n=0anznhas the radius of convergenceR[A]∈[1,+∞].For a heterogeneous differential equationz2w′′+ (β0z2+β1z)w′+ (γ0z2+γ1z+γ2)w=A(z)with complex parameters geometrical properties of its solutions (convexity, starlikeness and close-to-convexity) in the unit disk are investigated. Two cases are considered: ifγ26=0 andγ2=0. Wealso consider cases when parameters of the equation are realnumbers. Also we prove that for asolutionfof this equation the radius of convergenceR[f]equals toR[A]and the recurrent formulasfor the coefficients of the power series off(z)are found. For entire solutions it is proved that theorder of a solutionfis not less then the order ofA(̺[f]≥̺[A]) and the estimate is sharp. The sameinequality holds for generalized orders (̺αβ[f]≥̺αβ[A]). For entire solutions of this equation thebelonging to convergence classes is studied. Finally, we consider a linear differential equation of theendless order∞∑n=0ann!w(n)=Φ(z), and study a possible growth of its solutions.
On Hadamard compositions of Dirihlet series and Dirihlet series absolutely converging in half-plane
(2019) Mulyava, Oksana; Sheremeta, Miroslav
In terms of generalized orders the growth of this composition and their derivatives is investigated. A relation between the behavior of the maximal terms of the Hadamard composition of the derivatives and of the derivative of the Hadamard composition is established.
Remarks to relative growth of entire dirichlet series
(2019) Mulyava, Oksana; Sheremeta, Miroslav
The growth of F with respect to G is studied through the generalized order. Formulas are found for the finding these quantities.
On Hadamard composition of Gelfond-Leont’ev derivatives of entire and analytic functions in the unit disk
(2021) Mulyava, Oksana; Sheremeta, Miroslav
For an entire function and an analytic in the unit disk function the growth of the Hadamard composition of their Gelfond-Leont'ev derivatives is investigated in terms of generalized orders. A relationship between the behaviors of the maximal terms of Hadamard composition of Gelfond-Leont'ev derivatives and of the Gelfond-Leont'ev derivative of Hadamard composition is established.
On the Relative Growth of Dirichlet Series with Zero Abscissa of Absolute Convergence
(2021) Mulyava, Oksana
Let F and G be analytic functions given by Dirichlet series with exponents increasing to + ∞ and zero abscissa of absolute convergence.The growth of F with respect to G is studied through the generalized order. Formulas are found for the finding these quantities.
On belonging of characteristic functions of probability laws to a convergence class
(2013) Kulyavetc, Lubov; Mulyava, Oksana; Sheremeta, Miroslav
It is investigated the condition on a probability law, under which its characteristic function belongs to a convergence class. Досліджено умову на ймовірнісний закон відповідно до якого характеристична функція належить до класу збіжності.
Relation between the maximum modulus and the maximal term of Dirichlet series in terms of a convergence class
(2012) Mulyava, Oksana; Sheremeta, Miroslav; Sumyk, O.
A relation between the growth of maximum modulus and the growth maximal term of Dirichlet series in terms of a convergence class is investigated.Досліджено зв’язок між зростанням максимуму модуля і зростанням максимального члена ряду Діріхле в термінах класів збіжності.
On a convergence class for Dirichlet series
(2000) Mulyava, Oksana; Sheremeta, Miroslav
A relation between the maximum of the modulus, the maximal term and coefficients of Dirichlet series in terms of a convergence class is investigated. Досліджено зв’язок між максимумом модуля, максимальним членом і коефіцієнтами ряду Діріхле в термінах класів збіжності.
On belonging of Naftalevich-Tsuji products to a generalized convergence class
(2002) Gal, Yuriy; Mulyava, Oksana; Sheremeta, Miroslav
In terms of the zeros distribution, a class of Naftalevich-Tsuji products defined by the convergence of the integral is described, where and are positive continuous increasing to functions. В термінах розподілу нулів описаний клас добутків Нафталевича-Цудзі, визначений збіжністю інтеграла, де і – додатні неперервні зростаючі до функції.
A convergence class for entire Dirichlet series of slow growth
(2000) Mulyava, Oksana
For an entire Dirichlet series with nonnegative increasing to infinity exponents a connection between the growth of maximum modulus and the behavior of coefficients is established in the terms of certain convergence class.

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