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Erhan Deniz

Publications and source records attributed to Erhan Deniz.

14 recordsLinked to original sources
arXiv2023

Sharp coefficients bounds for Starlike functions associated with Gregory coefficients

In this paper we introduced the class $\mathcal{S}_{G}^{\ast }$ of analytic functions which is related with starlike functions and generating function of Gregory coefficients. By using bounds on some coefficient functionals for the family of functions with positive real part, we obtain for functions in the class $\mathcal{S}_{G}^{\ast }$ several sharp coefficient bounds on the first six coeffcients and also further sharp bounds on the corresponding Hankel determinants.

math.CV↗
arXiv2020

Geometric Properties of function $az^{2}J_{ν}^{\prime \prime }(z)+bzJ_{ν}^{\prime}(z)+cJ_{ν}(z)$

In this paper our aim is to find the radii of starlikeness and convexity for three different kind of normalization of the $N_ν(z)=az^{2}J_{ν}^{\prime \prime }(z)+bzJ_{ν}^{\prime}(z)+cJ_{ν}(z)$ function, where $J_ν(z)$ is called the Bessel function of the first kind of order $ν.$ The key tools in the proof of our main results are the Mittag-Leffler expansion for $N_ν(z)$ 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 $N_ν(z)$ function. Finally, we evaluate certain multiple sums of the zeros for $N_ν(z)$ function.

math.CV↗
arXiv2019

The solution of the Brannan conjecture

We make the final step to give a proof for the Brannan's conjecture. The basic tool of the study is a Mac-Laurin development and an adequately estimation of an integral.

math.CV↗
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↗
arXiv2017

The radius of uniform convexity of Bessel functions

In this paper, we determine the radius of uniform convexity for three kinds of normalized Bessel functions of the first kind. In the mentioned cases the normalized Bessel functions are uniformly convex on the determined disks. Moreover, necessary and sufficient conditions are given for the parameters of the three normalized functions such that they to be uniformly convex in the open unit disk. The basic tool of this study is the development of Bessel functions in function 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↗
arXiv2015

Differential Subordinations Involving Generalized Bessel Functions

In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some appropriate classes of admissible functions. We obtain also some sandwich-type results and we point out various known or new special cases of our main results.

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↗
arXiv2014

Close-to-convexity of normalized Dini functions

In this paper necessary and sufficient conditions are deduced for the close-to-convexity of some special combinations of Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and some newly discovered Mittag-Leffler expansions for Bessel functions of the first kind.

math.CA↗
arXiv2011

Univalence criteria related with Ruscheweyh and Salagean derivatives and Loewner Chains

In this paper we obtain, by the method of Loewner chains, some sufficient conditions for the analyticity and the univalence of the functions defined by an integral operator. These conditions in- volves Ruscheweyh and Salagean derivative operator in the open unit disk. In particular cases, we find the well-known conditions for univalency established by Becker [3], Ahlfors [2], Kanas and Srivastava [8] and others for analytic mappings f : U ! C: Also, we obtain the corresponding new, useful and simpler conditions for this integral operator.

math.CV↗
arXiv2010

Subclasses of meromorphically multivalent functions defined by a differential operator

In this paper we introduce and study two new subclasses Σ_{λμ mp}(α,β)$ and $Σ^{+}_{λμmp}(α,β)$ of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of $% (n,δ)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.

math.CV↗
arXiv2010

Certain subclasses of multivalent functions defined by new multiplier transformations

In the present paper the new multiplier transformations $\mathrm{{\mathcal{J}% }}_{p}^{δ}(λ,μ,l)$ $(δ,l\geq 0,\;λ\geq μ\geq 0;\;p\in \mathrm{% }%\mathbb{N} )}$ of multivalent functions is defined. Making use of the operator $\mathrm{% {\mathcal{J}}}_{p}^{δ}(λ,μ,l),$ two new subclasses $\mathcal{% P}_{λ,μ,l}^{δ}(A,B;σ,p)$ and $\widetilde{\mathcal{P}}% _{λ,μ,l}^{δ}(A,B;σ,p)$\textbf{\ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $\mathcal{P}_{λ,μ,l}^{δ}(A,B;σ,p)$ and $\widetilde{\mathcal{P}}_{λ,μ,l}^{δ}(A,B;σ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.

math.CV↗