Poisson distribution series on a general class of analytic functions

The main object of this paper is to find necessary and sufficient conditions for the Poisson distribution series to be in a general class of analytic functions with negative coefficients. Further, we consider an integral operator related to the Poisson distribution series to be in this class. A number of known or new results are shown to follow upon specializing the parameters involved in our main results

Coefficients bounds for a family of bi-univalent functions defined by Horadam polynomials

In the present paper, we determine upper bounds for the first two Taylor–Maclaurin coefficients |a2| and |a3| for a certain family of holomorphic and bi-univalent functions defined by using the Horadam polynomials. Also, we solve Fekete–Szegö problem of functions belonging to this family. Further, we point out several special cases of our results

Starlikeness of a new general integral operator for meromorphic multivalent functions

In the present paper, we introduce a new general integral operator of meromorphic multivalent functions. The starlikeness of this integral operator is determined. Several special cases are also discussed in the form of corollaries

Univalence of integral operators involving Bessel functions

AbstractIn this note our aim is to deduce some sufficient conditions for integral operators involving Bessel functions of the first kind to be univalent in the open unit disk. The key tools in our proofs are the generalized versions of the well-known Ahlfors’ and Becker’s univalence criteria and some inequalities for the normalized Bessel functions of the first kind

<i>n</i>-Quasi-<i>m</i>-Complex Symmetric Transformations

Our aim in this study is to consider a generalization of the concept of m-complex symmetric transformations to n-quasi-m-complex symmetric transformations. A map S∈B(Y) is said to be an n-quasi-m-complex symmetric transformation if there exists a conjugation C on Y such that S satisfies the condition S*n∑0≤k≤m(−1)m−kmkS*kCSm−kCSn=0, for some positive integers n and m. This class of transformation contains the class of m-complex symmetric transformations as a proper subset. Some basic structural properties of n-quasi-m-complex symmetric linear transformations are established with the help of transformation matrix representation. In particular, we obtain that a power of an n-quasi-m-complex symmetric is again an n-quasi-m-complex symmetric operator. Moreover, if T and S are such that T is an n1-quasi-m1-complex symmetric and S is an n2-quasi-m2-complex symmetric, their product TS is an max{n1,n2}-quasi-(m1+m2−1)-complex symmetric under suitable conditions. We examine the stability of n-quasi-m-complex symmetric operators under perturbation by nilpotent operators