Class Of Meromorphic Functions Research Articles

INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK

In this paper, we consider a class of meromorphic functions \(r(z)\) having an \(s\)-fold zero at the origin and establish some inequalities of Bernstein and Turán type for the modulus of the derivative of rational functions in the sup-norm on the disk in the complex plane. These results produce some sharper inequalities while taking into account the placement of zeros of the underlying rational function. Moreover, many inequalities for polynomials and polar derivatives follow as special cases. In particular, our results generalize as well as refine a result due Dewan et al. [6].

BOUNDS FOR FUNCTIONALS DEFINED ON A CERTAIN CLASS OF MEROMORPHIC FUNCTIONS

AbstractWe obtain bounds for certain functionals defined on a class of meromorphic functions in the unit disc of the complex plane with a nonzero simple pole. These bounds are sharp in a certain sense. We also discuss possible applications of this result. Finally, we generalise the result to meromorphic functions with more than one simple pole.

Preserving Classes of Meromorphic Functions through Integral Operators

We consider three new classes of meromorphic functions defined by an extension of the Wanas operator and two integral operators, in order to study some preservation properties of the classes. The purpose of the paper is to find the conditions such that, when we apply the integral operator Jp,γ to some function from the new defined classes ΣSp,qn(α,δ), respectively ΣSp,qn(α), we obtain also a function from the same class. We also define a new integral operator on the class of meromorphic functions, denoted by Jp,γ,h, where h is a normalized analytic function on the unit disc. We study some basic properties of this operator. Then we look for the conditions which allow this operator to preserve a particular subclass of the classes mentioned above.

On the uniqueness of two different classes of meromorphic functions under the sharing of two sets of rational functions

We study the uniqueness problem of two special classes of meromorphic functions sharing two sets of small functions. One of the considered classes has the property to include the Selberg class L functions, while the other class is comprising of arbitrary meromorphic functions having finitely many poles. We obtain a number of results which extend and improve a number of earlier results such as Li [ Proc. Amer. Math. Soc., 138 (2010), 2071-2077], Lin and Lin [Filomat 30 (2016), 3795-3806] and others. We have also been able to replace the strict CM (IM) sharing of the sets in our theorems to almost CM (almost IM) sharing.

Some Properties of Mesomorphic Univalent Functions with Negative Coefficients Defined

The main aim of the present investigation is to introduce a new class of meromorphic univalent functions with negative coefficients defined by Dziok-Srivastava operator. Some geometric properties are introduced, like coefficient estimate, integral operator, Feket-Szegӧ bounds for this class of meromorphic functions.

Polynomial of a meromorphic function and its k-th derivative sharing a set

With the help of weighted sharing of sets, we find out the class of meromorphic functions f, when P(f) and [P(f)](k) share a set Sm of small functions. Our results improve and extend the results of Zhang and Yang [Ann. Acad. Sci. Fenn. Math. 34 (2009), 249-260] and Xu et al. [Rev. Mat. Teor. Apl. 23(1) (2016), 291-308]. A number of examples are exhibited to validate certain claims of the main results.

Unique range sets of meromorphic functions of non-integer finite order

This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, it provides an answer to a question posed by Gross for a particular class of meromorphic functions. Moreover, some observations are made on some results due to Sahoo and Karmakar, Acta Univ. Sapient. Math., doi:10.2478/ausm-2018-0025; Sahoo and Sarkar, Bol. Soc. Mat. Mex., doi:10.1007/s40590-019-00260-4.

On Some Classes with Norms of Meromorphic Function Spaces Defined by General Spherical Derivatives

The main concerned target of this article is to define and study some concerned classes of meromorphic function spaces using the general spherical derivatives. The general Besov-type classes of meromorphic functions as well as the general normal functions are considered intensively and both are compared deeply with each other. Specifically, multiple results concerning general meromorphic-type classes as well as non-normal classes are obtained by the help of general spherical derivatives. The concerned results are proved by constructing some specific mild conditions on the sequences of points belonging to the concerned meromorphic-type classes. The obtained results generalize and improve the corresponding previous results in some concerned respects. The concerned proofs and methods are simply presented.

NEW SUBCLASS OF MEROMORPHIC FUNCTIONS BY THE GENERALIZATION OF THE q-DERIVATIVE OPERATOR

In this paper, we introduce a new class of meromorphic functions, using the exponent $ q $-derivative operator, and then look at it coefficient estimates, extreme points, convex linear combination, Radii of starlikeness, convexity and finally partial sum property are investigated.

Application of Quasisubordination to Certain Classes of Meromorphic Functions

Inequalities play a fundamental role in many branches of mathematics and particularly in real analysis. By using inequalities, we can find extrema, point of inflection, and monotonic behavior of real functions. Subordination and quasisubordination are important tools used in complex analysis as an alternate of inequalities. In this article, we introduce and systematically study certain new classes of meromorphic functions using quasisubordination and Bessel function. We explore various inequalities related with the famous Fekete-Szego inequality. We also point out a number of important corollaries.

On classes of meromorphic functions with fixed point and fixed second and finitely many coeeficients defined by q -Derivative

Abstract: In this paper we consider the class functions with a fixed point The aim of the present paper is to drive several interesting properties as coefficient estimates, distortion M S ( , , c).The q    theorems, radii of starlikeness and convexity and closure theorems of f (z) in the class results are generalized to families with finitely many fixed coefficients

University of Montenegro, Podgorica, Montenegro

Using dynamic and geometry of Möebious mappings we prove Lindelöf type theorems for much larger class of functions on the unit disk than previously considered class of meromor-phic functions.

Meromorphic Starlike Functions with Respect to Symmetric Points

The main purpose of this article is to introduce a class of meromorphic functions associated with the symmetric points in circular domain. We investigate the necessary and sufficient conditions, distortions theorem for this class. Furthermore, we obtain closure and convolutions properties, radii of starlikeness and partial sum results for these functions.

Bounds for the Coefficient of Faber Polynomial of Meromorphic Starlike and Convex Functions

Let Σ be the class of meromorphic functions f of the form f ( ζ ) = ζ + ∑ n = 0 ∞ a n ζ − n which are analytic in Δ : = { ζ ∈ C : | ζ | > 1 } . For n ∈ N 0 : = N ∪ { 0 } , the nth Faber polynomial Φ n ( w ) of f ∈ Σ is a monic polynomial of degree n that is generated by a function ζ f ′ ( ζ ) / ( f ( ζ ) − w ) . For given f ∈ Σ , by F n , i ( f ) , we denote the ith coefficient of Φ n ( w ) . For given 0 ≤ α < 1 and 0 < β ≤ 1 , let us consider domains H α and S β ⊂ C defined by H α = { w ∈ C : Re ( w ) > α } and S β = { w ∈ C : | arg ( w ) | < β } , which are symmetric with respect to the real axis. A function f ∈ Σ is called meromorphic starlike of order α if ζ f ′ ( ζ ) / f ( ζ ) ∈ H α for all ζ ∈ Δ . Another function f ∈ Σ is called meromorphic strongly starlike of order β if ζ f ′ ( ζ ) / f ( ζ ) ∈ S β for all ζ ∈ Δ . In this paper we investigate the sharp bounds of F n , n − i ( f ) , n ∈ N 0 , i ∈ { 2 , 3 , 4 } , for meromorphic starlike functions of order α and meromorphic strongly starlike of order β . Similar estimates for meromorphic convex functions of order α ( 0 ≤ α < 1 ) and meromorphic strongly convex of order β ( 0 < β ≤ 1 ) are also discussed.

On a certain classes of meromorphic functions with positive coefficients

In this paper certain classes of meromorphic functions in punctured unit disk are defined. Some properties including coefficient inequalities, convolution and other results are investigated.

Bernstein-type inequalities for certain class of meromorphic functions

In this paper, we shall obtain some Bernstein-type inequalities for certain class of meromorphic functions with restricted zeros and prescribed poles. Our results extend some well known polynomial inequalities to a class of rational functions.

On some results for a class of meromorphic functions having quasiconformal extension

We consider the class $$\Sigma (p)$$ of univalent meromorphic functions f on $${\mathbb D}$$ having a simple pole at $$z=p\in [0,1)$$ with residue 1. Let $$\Sigma _k(p)$$ be the class of functions in $$\Sigma (p)$$ which have k-quasiconformal extension to the extended complex plane $${\hat{\mathbb C}}$$ , where $$0\le k < 1$$ . We first give a representation formula for functions in this class and using this formula, we derive an asymptotic estimate of the Laurent coefficients for the functions in the class $$\Sigma _k(p)$$ . Thereafter, we give a sufficient condition for functions in $$\Sigma (p)$$ to belong to the class $$\Sigma _k(p).$$ Finally, we obtain a sharp distortion result for functions in $$\Sigma (p)$$ and as a consequence, we obtain a distortion estimate for functions in $$\Sigma _k(p).$$

Coefficients inequalities for classes of meromorphic functions

Coefficients inequalities for classes of meromorphic functions

Hirzebruch Functional Equation: Classification of Solutions

The Hirzebruch functional equation is $$\sum\nolimits_{i = 1}^n {\prod\nolimits_{j \ne i} {(1/f({z_j} - {z_i})) = c} } $$ with constant c and initial conditions f(0) = 0 and f'(0) = 1. In this paper we find all solutions of the Hirzebruch functional equation for n ≤ 6 in the class of meromorphic functions and in the class of series. Previously, such results have been known only for n ≤ 4. The Todd function is the function determining the two-parameter Todd genus (i.e., the χa,b-genus). It gives a solution to the Hirzebruch functional equation for any n. The elliptic function of level N is the function determining the elliptic genus of level N. It gives a solution to the Hirzebruch functional equation for n divisible by N. A series corresponding to a meromorphic function f with parameters in U ⊂ ℂk is a series with parameters in the Zariski closure of U in ℂk, such that for the parameters in U it coincides with the series expansion at zero of f. The main results are as follows: (1) Any series solution of the Hirzebruch functional equation for n = 5 corresponds either to the Todd function or to the elliptic function of level 5. (2) Any series solution of the Hirzebruch functional equation for n = 6 corresponds either to the Todd function or to the elliptic function of level 2, 3, or 6. This gives a complete classification of complex genera that are fiber multiplicative with respect to ℂPn−1 for n ≤ 6. A topological application of this study is an effective calculation of the coefficients of elliptic genera of level N for N = 2,..., 6 in terms of solutions of a differential equation with parameters in an irreducible algebraic variety in ℂ4.

Nonlinear mixed Cherepanov boundary-value problem

ABSTRACTWe consider a nonlinear boundary-value problem consisting in the determination of a function that is meromorphic in the upper half-plane, satisfies the homogeneous Hilbert boundary condition on the set L of n intervals of the real axis and has a given module on the set . This problem was stated and solved in Cherepanov. Cherepanov proved that the required solution with a given number and location of its interior zeros and poles and with integrable singularities at all endpoints of L exists if and only if n−1 solvability conditions are satisfied. We prove that this problem is unconditionally solvable. A particular solution, , is found in the class of meromorphic functions with a properly chosen location of n−1 zeros and poles. Namely, we have shown that these zeros and poles are defined as the solution of some solvable real analogue of the Jacobi inversion problem. A general meromorphic solution of the Cherepanov problem is obtained with the help of the particular solution . The problem of a possible decrease in the number of zeros and poles of the desired solution is investigated.