Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRadii of the $beta -$uniformly convex of order $alpha$ of Lommel and Struve functions
51
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we determine the radii of $beta -$uniformly convex of order $alpha $ for three kinds of normalized Lommel and Struve functions of the first kind. In the cases considered the normalized Lommel and Struve functions are $beta -$uniformly convex functions of order $alpha $ on the determined disks. The basic tool of this study is Lommel and Struve functions in series.
rate research
Read More
In this paper our aim is to determine the radii of univalence, starlikeness and convexity of the normalized regular Coulomb wave functions for two different kinds of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for regular Coulomb wave functions, and properties of zeros of the regular Coulomb wave functions and their derivatives. Moreover, by using the technique of differential subordinations we present some conditions on the parameters of the regular Coulomb wave function in order to have a starlike normalized form. In addition, by using the Euler-Rayleigh inequalities we obtain some tight bounds for the radii of starlikeness of the normalized regular Coulomb wave functions. Some open problems for the zeros of the regular Coulomb wave functions are also stated which may be of interest for further research.
In the present investigation the authors obtain upper bounds for the second Hankel determinant of the classes bi-starlike and bi-convex functions of order beta.
A motivation comes from {em M. Ismail and et al.: A generalization of starlike functions, Complex Variables Theory Appl., 14 (1990), 77--84} to study a generalization of close-to-convex functions by means of a $q$-analog of a difference operator acting on analytic functions in the unit disk $mathbb{D}={zin mathbb{C}:,|z|<1}$. We use the terminology {em $q$-close-to-convex functions} for the $q$-analog of close-to-convex functions. The $q$-theory has wide applications in special functions and quantum physics which makes the study interesting and pertinent in this field. In this paper, we obtain some interesting results concerning conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in the $q$-close-to-convex family. As a result we find certain dilogarithm functions that are contained in this family. Secondly, we also study the famous Bieberbach conjecture problem on coefficients of analytic $q$-close-to-convex functions. This produces several power series of analytic functions convergent to basic hypergeometric functions.
The theory of $q$-analogs frequently occurs in a number of areas, including the fractals and dynamical systems. The $q$-derivatives and $q$-integrals play a prominent role in the study of $q$-deformed quantum mechanical simple harmonic oscillator. In this paper, we define a symmetric $q$-derivative operator and study new family of univalent functions defined by use of that operator. We establish some new relations between functions satisfying analytic conditions related to conical sections.
In this paper, two new subclasses of bi-univalent functions related to conic domains are defined by making use of symmetric $q$-differential operator. The initial bounds for Fekete-Szego inequality for the functions $f$ in these classes are estimated.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
