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Murat Çağlar

Publications and source records attributed to Murat Çağlar.

10 recordsLinked to original sources
arXiv2018

Geometric Properties of Bessel function derivatives

In this paper our aim is to find the radii of starlikeness and convexity of Bessel function derivatives for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for nth derivative of Bessel function and properties of real zeros of it. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized nth derivative of Bessel function. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind.

math.CV↗
arXiv2017

Radii of the $β-$uniformly convex of order $α$ of Lommel and Struve functions

In this paper, we determine the radii of $β-$uniformly convex of order $α$ for three kinds of normalized Lommel and Struve functions of the first kind. In the cases considered the normalized Lommel and Struve functions are $β-$uniformly convex functions of order $α$ on the determined disks. The basic tool of this study is Lommel and Struve functions in series.

math.CV↗
arXiv2016

Radii of starlikeness and convexity of regular Coulomb wave functions

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.

math.CV↗
arXiv2014

Starlikeness of Bessel functions and their derivatives

In this paper necessary and sufficient conditions are deduced for the starlikeness of Bessel functions of the first kind and their derivatives of the second and third order by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and some Mittag-Leffler expansions for the derivatives of Bessel functions of the first kind, as well as some results on the zeros of these functions.

math.CA↗
arXiv2013

Some sufficient conditions for the univalence of an integral operator

Making use of the method of subordination chains, we obtain some sufficient conditions for the univalence of an integral operator. In particular, as special cases, our results imply certain known univalence criteria. A refinement to a quasiconformal extension criterion of the main result, is also obtained.

math.CV↗
arXiv2013

Univalence Criteria and Quasiconformal Extensions

In the present paper, we obtain a more general conditions for univalence of analytic functions in the open unit disk U. Also, we obtain a refinement to a quasiconformal extension criterion of the main result.

math.CV↗
arXiv2012

Coefficient bounds for new subclasses of bi-univalent functions

In the present investigation, we consider two new subclasses N_{Σ}^{μ}(α,λ) and N_{Σ}^{μ}(β,λ) of bi-univalent functions defined in the open unit disk U={z:|z|<1}. Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.

math.CV↗