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Halit Orhan

Publications and source records attributed to Halit Orhan.

At least 19 recordsLinked to original sources
arXiv2026

Functional inequalities for starlike and convex functions associated with $g$-derivative operator

In this paper we first introduce a new class of derivative operators, termed $g$-derivative operators, which unifies the $q$-derivative, $(p,q)$-derivative and $(\alpha,\beta,\gamma)$-derivative operators, even classical derivative in the literature. Based on this generalized framework, we define two novel function classes, specifically $g$-starlike functions and $g$-convex functions. Further, we employ the subordination principle of analytic functions to conduct the coefficient estimations for such function classes, and subsequently derive the bounds for the corresponding Fekete-Szeg\"{o} inequality, Toeplitz determinants and Hankel determinants.

math.CV↗
arXiv2023

On the symmetric $q$-analog on the bi-univalent functions with respect to symmetric points

Our objective is to usher and investigate the subclass$\widetilde{\mathcal{S^{*}_{\sum}}}^{\eta}_{q}(\mu,\lambda;\phi)$ of the function class $\sum$ of analytic and bi-univalent functions related with the symmetric $q$-derivative operator and the generalized Bernardi integral operator. On the one hand, without the generalized Bernardi integral operator we estimate the second Hankel determinants for the reduced subclasses $\widetilde{\mathcal{S^{*}_{\sum}}}_{q}(\lambda;\phi)$ with respect to symmetric points. On the other hand, we also give the corresponding results of Fekete-Szeg\"{o} functional inequalities and the upper bounds of the coefficients $a_2$ and $a_3$ for these subclasses.

math.CV↗
arXiv2018

Radius of Uniform Convexity of some special functions

In this investigation our main aim is to determine the radius of uniform convexity of the some normalized q-Bessel and Wright functions. Here we consider six different normalized forms of q-Bessel functions, while we apply three different kinds of normalizations of Wright function. Also, we have shown that the obtained radii are the smallest positive roots of some functional equations.

math.CV↗
arXiv2017

On partial sums of normalized q-Bessel functions

In the present investigation our main aim is to give lower bounds for the ratio of some normalized $q$-Bessel functions and their sequences of partial sums. Especially, we consider Jackson's second and third $q$-Bessel functions and we apply one normalization for each of them.

math.CA↗
arXiv2017

Bounds for radii of convexity of some $q$-Bessel functions

In the present investigation, by applying two different normalizations of the Jackson and Hahn-Exton $q$-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-P\'olya class of real entire functions plays an important role in this work.

math.CV↗
arXiv2016

Bounds for radii of starlikeness and convexity of some special functions

In this paper we consider some normalized Bessel, Struve and Lommel functions of the first kind, and by using the Euler-Rayleigh inequalities for the first positive zeros of combination of special functions we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalization of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In addition, by using some ideas of Ismail and Muldoon we present some new lower and upper bounds for the zeros of derivatives of some normalized Struve and Lommel functions. The Laguerre-P\'olya class of real entire functions plays an important role in our study.

math.CA↗
arXiv2016

Partial sums of the normalized Dini functions

Let $\left( w_{\alpha ,v}\right) _{m}(z)=z+\sum\limits_{n=1}^{m}a_{n}z^{n+1} $ be the sequence of partial sums of normalized Dini functions $w_{\alpha ,v}(z)=z+\sum\limits_{n=1}^{\infty }a_{n}z^{n+1}$ where $a_{n}=\frac{\left( -1\right) ^{n}\left( 2n+\alpha \right) }{\alpha 4^{n}n!\left( v+1\right) _{n}% }$. The aim of the present paper is to obtain lower bounds for $\mathcal{R} \left\{ \frac{w_{\alpha ,v}(z)}{\left( w_{\alpha ,v}\right) _{m}(z)}\right\} ,$ $\mathcal{R}\left\{ \frac{\left( w_{\alpha ,v}\right) _{m}(z)}{w_{\alpha ,v}(z)}\right\} ,$ $\mathcal{R}\left\{ \frac{w_{\alpha ,v}^{^{\prime }}(z)}{ \left( w_{\alpha ,v}\right) _{m}^{^{\prime }}(z)}\right\}$ and $\mathcal{R} \left\{ \frac{\left( w_{\alpha ,v}\right) _{m}^{^{\prime }}(z)}{w_{\alpha ,v}^{^{\prime }}(z)}\right\}$ . Also we give a few geometric description regarding image domains of some functions.

math.CV↗
arXiv2014

The radius of $\alpha$-convexity of normalized Bessel functions of the first kind

The radii of $\alpha$-convexity are deduced for three different kind of normalized Bessel functions of the first kind and it is shown that these radii are between the radii of starlikeness and convexity, when $\alpha\in[0,1],$ and they are decreasing with respect to the parameter $\alpha.$ The results presented in this paper unify some recent results on the radii of starlikeness and convexity for normalized Bessel functions of the first kind. The key tools in the proofs are some interlacing properties of the zeros of some Dini functions and the zeros of Bessel functions of the first kind.

math.CA↗
arXiv2014

Radii of starlikeness of some special functions

Geometric properties of the classical Lommel and Struve functions, both of the first kind, are studied. For each of them, there different normalizations are applied in such a way that the resulting functions are analytic in the unit disc of the complex plane. For each of the six functions we determine the radius of starlikeness precisely.

math.CA↗
arXiv2014

Fekete-Szeg\"o problem for certain classes of Ma-Minda bi-univalent functions

In the present work, we propose to investigate the Fekete-Szeg\"o inequalities certain classes of analytic and bi-univalent functions defined by subordination. The results in the bounds of the third coefficient which improve many known results concerning different classes of bi-univalent functions. Some interesting applications of the results presented here are also discussed.

math.CV↗
arXiv2012

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

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↗
arXiv2012

On neighborhood and partial sums problem for generalized Sakaguchi type functions

In the present investigation, we introduce a new class k-US_{s}^{{\eta}}({\lambda},{\mu},{\gamma},t) of analytic functions in the open unit disc U with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions f(z) belonging to this class.

math.CV↗
arXiv2012

Coefficient bounds for new subclasses of bi-univalent functions

In the present investigation, we consider two new subclasses N_{{\Sigma}}^{{\mu}}({\alpha},{\lambda}) and N_{{\Sigma}}^{{\mu}}({\beta},{\lambda}) 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↗