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Radii of starlikeness and convexity of generalized k-Bessel functions

Toklu Evrim

Journal of Applied Analysis

2023

Vol. 29, nr 1

171--185

The main purpose of this study is to determine the radii of starlikeness and convexity of the generalized k-Bessel functions for three different kinds of normalization in such away that the resulting functions are analytic in the unit disk of the complex plane. The characterization of entire functions from Laguerre-Pólya class plays a significant role in this paper. Moreover, the interlacing properties of the zeros of the k-Bessel function and its derivative is also useful in the proof of the main results. By making use of the Euler-Rayleigh inequalities for the real zeros of the generalized k-Bessel function, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero.

Certain inequalities of meromorphic univalent functions associated with the Mittag-Leffler function

Aouf Mohamed K., Mostafa Adela O.

Journal of Applied Analysis

2019

Vol. 25, nr 2

173--178

The purpose of this paper is to prove differential inequalities for meromorphic univalent functions by using a new operator associated with the Mittag-Leffler function.

Radius of convexity of sections of a class of close-to-convex functions of order α

Banu B. U., Youvaraj G. P

Fasciculi Mathematici

2018

Nr 60

29--35

In this paper we study radius of convexity of sections of a class of univalent close-to-convex functions on D = { z ∈ C : |z| < 1}. For functions in this class, coefficient bounds, an integral representation and radius of convexity of nth sections have been obtained.

Partial sums of a certain harmonic univalent meromorphic functions

Aouf M. K., El-Ashwah R. M., Dziok J., Stankiewicz J.

Journal of Mathematics and Applications

2014

Vol. 37

5--12

In the present paper we determine sharp lower bounds of the real part of the ratios of harmonic univalent meromorphic functions to their sequences of partial sums [...].

A unified representation of some starlike and convex harmonic functions with negative coefficients

El-Ashwah R. M., Aouf M. K., Hassan A. A. M., Hassan A. H.

Opuscula Mathematica

2013

Vol. 33, no. 2

273--281

In this paper we introduce a unified representation of starlike and convex harmonic functions with negative coefficients, related to uniformly starlike and uniformly convex analytic functions. We obtain extreme points, distortion bounds, convolution conditions and convex combinations for this family.

On harmonic univalent mappings with small coefficients

Ganczar A.

Demonstratio Mathematica

2001

Vol. 34, nr 3

548-558