Sufficient conditions for integral operator defined by Bessel functions

Sufficient Conditions for Integral Operator Defined by Bessel Functions

The main object of the present paper is to derive several sufficient conditions for integral operator defined by Bessel functions of the first kind to be convex and strongly convex of given order in the open unit disk.

Some Properties of an Integral Operator Defined by Bessel Functions

In this paper we will study the integral operator involving Bessel functions of the first kind and of order v.We will investigate the integral operator for the classes of starlike and convex functions in the open unit disk.

Sufficient Conditions for Univalence of an Integral Operator Defined by Al-Oboudi Differential Operator

Bi-concave Functions Defined by Al-Oboudi Differential Operator

The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

Ozaki's conditions for general integral operator

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...