A new subclass of meromorphic functions with positive coefficients

In the present paper, we consider the new subclass of Meromorphic functions with positive coefficients and obtain a necessary and sufficient condition for a function f to be in this class. We obtain distortion properties, radius of convexity, starlikeness, convex linear combinations for the function f in this class.     

Coefficient estimates for certain classes of meromorphic bi-univalent functions

We define a new class of meromorphic bi-univalent functions and use the Faber polynomial expansions to determine the coefficient bounds for such functions. Our results generalize and/or improve some of the previously known results. A meromorphic function is said to be bi-univalent in a given domain Δ if both the function and its inverse map are univalent there.     

On certain subclasses of meromorphic functions associated with certain differential operators

In this work, we study some subordination and convolution properties of certain subclasses of meromorphic functions which are defined by a previously mentioned differential operator.     

Some applications of Miller-Mocanu lemma on certain classes of meromorphic functions

In this paper, making use of a linear operator we introduce and study certain new classes of meromorphic functions. We derive some inclusion results. These classes contain many known classes as a special case.     

The value regions of initial coefficients in a certain class of meromorphic functions

Let M_k,λ(0≤λ≤1, k≥2) be the class of functions f(z)=1/z+a_o+a₁z+... that are regular and locally univalent for 0<⩛z⩛<1 and satisfy the condition where J_λ(z)=λ(1+zf″(z)/f'(z))+(1-λ)zf'(z)/f(z). In the class M_k,λ we consider sorne coefficient problems and problems concerning distortion theorems. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 91–96. Translated by N. Yu. Netsvetaev.     

On certain classes of analytic functions

In this paper we introduce some new classes of analytic functions which generalise several known sequence spaces and function spaces studied by Simons, Maddox, Srivastava and others. We establish some inclusion relations, topological results and give the characterisation of continuous linear functionals for these spaces. Our results include the corresponding results of Simons, Maddox and others.     

On a subclass of certain k-starlike functions with negative coefficients

The aim of the present paper is to show some properties of functions belonging to the class (k, n, α)− . The obtained results extend the results by Silverman [3].     

Structure and the coefficients of certain classes of regular functions

In this paper, the well-known results of Carathéodory, Toeplitz, F. Riesz, Herglotz, containing the characterization of the Carathéodory class with the aid of the Stieltjes integral and with the aid of nonnegative quadratic forms (conditions on the coefficients), are extended to certain other classes of functions, regular in a circle or in an annulus.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 47–57, 1983.     

On deficient values of meromorphic functions satisfying a certain functional equation

Aequationes mathematicae -     

Iteration of certain exponential-like meromorphic functions

The dynamics of functions \(f_\lambda (z)= \lambda \frac{\mathrm{e}^{z}}{z+1}\ \text{ for }\ z\in \mathbb {C}, \lambda >0\) is studied showing that there exists \(\lambda ^* > 0\) such that the Julia set of \(f_\lambda \) is disconnected for \(0< \lambda < \lambda ^*\) whereas it is the whole Riemann sphere for \(\lambda > \lambda ^*\). Further, for \(0< \lambda < \lambda ^*\), the Julia set is a disjoint union of two topologically and dynamically distinct completely invariant subsets, one of which is totally disconnected. The union of the escaping set and the backward orbit of \(\infty \) is shown to be disconnected for \(0<\lambda < \lambda ^*\) whereas it is connected for \(\lambda > \lambda ^*\). For complex \(\lambda \), it is proved that either all multiply connected Fatou components ultimately land on an attracting or parabolic domain containing the omitted value of the function or the Julia set is connected. In the latter case, the Fatou set can be empty or consists of Siegel disks. All these possibilities are shown to occur for suitable parameters. Meromorphic functions \(E_n(z) =\mathrm{e}^{z}(1+z+\frac{z^2}{2!}+\cdots +\frac{z^n}{n!})^{-1}\), which we call exponential-like, are studied as a generalization of \(f(z)=\frac{\mathrm{e}^{z}}{z+1}\) which is nothing but \(E_1(z)\). This name is justified by showing that \(E_n\) has an omitted value 0 and there are no other finite singular value. In fact, it is shown that there is only one singularity over 0 as well as over \(\infty \) and both are direct. Non-existence of Herman rings are proved for \(\lambda E_n \).     

Ranges of certain system of functionals in classes of functions with a positive real part

We give the algebraic characteristics of the range of the system C_p, C_2p, ..., c_np f() ( fixed, 0<¦¦<1, n1, P=1, 2, ...) on certain subclasses C_m,p, of the class C of functions, regular in the circle ¦z¦<1 and satisfying in it the condition Re f(z)>0. As an application one finds the range of f() on the subclasses C _m,p, ⁽ⁿ⁾ of functions from C_m,p, with prescribed coefficients c_p c_2p, ..., c_np.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 100, pp. 17–25, 1980.     

On eigenvalues for certain classes of positive operators

Mathematical Notes - Spectral gaps are estimated for some classes of positive operators with a group of leading eigenvalues. Such an analysis is based on passing to associated operators and using...