On New Bijective Convolution Operator Acting for Analytic Functions

It is well known that there are two important classes of analytic functions of Ma-Minda type (MMT): Ma-Minda starlike and Ma-Minda convex functions. In this work, we suggest a new class of analytic functions, which is normalized in the open unit disk. The suggested class is generated by a roulette curve formula, which satisfies the symmetric behavior in the open unit disk. A roulette curve is shaped as the path outlined by the sum of two complex numbers, each affecting at a uniform rapidity in a circle. Special cases are illustrated involving special functions. Graphics of the curve are illustrated by using Mathematica 13.3.

The study on fractional integrals of confluent hypergeometric functions provides interesting subordination and superordination results and inspired the idea of using this operator to introduce a new class of analytic functions. Given the class of functions An=f∈HU:fz=z+an+1zn+1+…,z∈U written simply A when n=1, the newly introduced class involves functions f∈A considered in the study due to their special properties. The aim of this paper is to present the outcomes of the study performed on the new class, which include a coefficient inequality, a distortion theorem and extreme points of the class. The starlikeness and convexity properties of this class are also discussed, and partial sums of functions from the class are evaluated in order to obtain class boundary properties.

The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U×U¯ having as coefficients holomorphic functions in U¯. Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯),f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}. This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential superordinations concerning the operator Lαm are established and the best subordinant is given for each strong differential superordination.

We introduce a new class of analytic functions on the unit disc of the complex plane by modifying the F(p, q, s) spaces introduced by the last author by adding a measure factor. We prove some basic properties and relationships with other classical function spaces

<abstract><p>The present investigation focus on applying the theories of differential subordination, differential superordination and related sandwich-type results for the study of some subclasses of symmetric functions connected through a linear extended multiplier operator, which was previously defined by involving the $ q $-Choi-Saigo-Srivastava operator. The aim of the paper is to define a new class of analytic functions using the aforementioned linear extended multiplier operator and to obtain sharp differential subordinations and superordinations using functions from the new class. Certain subclasses are highlighted by specializing the parameters involved in the class definition, and corollaries are obtained as implementations of those new results using particular values for the parameters of the new subclasses. In order to show how the results apply to the functions from the recently introduced subclasses, numerical examples are also provided.</p></abstract>

In this paper, using Hadmard product, we introduce certain new classes of analytic functions in the open unit disk. Such results as inclusion and subordination relationships, characterization and coecient estimates, growth and distortion theorems, extreme points, closure theorems and radius of starlikeness and convexity belonging to the class TS(f;g;;;;A;B ) are obtained. Further subordination results for the class S(f;g;;;;A;B ) are derived:

Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

The aim of the present paper is to introduce a new class of analytic functions by using a q-integral operator in the conic region. It is worth mentioning that these regions are symmetric along the real axis. We find the coefficient estimates, the Fekete–Szegö inequality, the sufficiency criteria, the distortion result, and the Hankel determinant problem for functions in this class. Furthermore, we study the inverse coefficient estimates for functions in this class.

Introduction: : In this work, we introduce and investigate a new class of analytic functions in the open unit disc with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions belonging to this class.

We discuss the best linear approximation methods in the Hardy spaceH q q≥1, for classes of analytic functions studied by N. Ainulloev; these are generalizations (in a certain sense) of function sets introduced by L. V. Taikov. The exact values of their linear and Gelfandn-widths are obtained. The exact values of the Kolmogorov and Bernsteinn-widths of classes of analytic (in |z|<1) functions whose boundaryK-functionals are majorized by a prescribed functions are also obtained.

Majorization properties for certain classes of analytic functions using the Sălăgean operator

Problem statement: The problem of giving sufficient condition for certain class of meromorphic functions defined as differential operator was studied. Approach: The differential operator of meromorphic functions containing fractional power was proposed and defined. The preliminary concept of subordination was introduced to give sharp proofs for certain sufficient conditions of the differential operator aforementioned. Results: Having new operator, subordination theorems established by using standard concept of subordination and reduced to well-known results studied by various researchers. The operator was then applied for fractional calculus and obtained new subordination theorem. Conclusion: Therefore, by having new operators, new criteria and new set of subordination theorems could be obtained with some earlier results and standard methods.

On some applications of a subordination theorem

The aim of this paper is to study the properties of a subclass of analytic functions related to p-valent Bazilevic functions by using the concept of differential subordination. We investigate some results concerned with coefficient bounds, inclusion results, radius problem, covering theorem, angular estimation of a certain integral operator, and some other interesting properties.

In this paper, we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients. The motivation of this paper is to generalize the Coefficient Estimates obtained by Attiya, and Aouf et al. by making use of the generalized differential operator Dnλ, μ.