Browsing by Author "Caglar, Murat"

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Applications of Q-Derivative Operator to Subclasses of Bi-Univalent Functions Involving Gegenbauer Polynomials
(Taylor & Francis Ltd, 2022) Hu, Qiuxia; Shaba, Timilehin Gideon; Younis, Jihad; Khan, Bilal; Mashwani, Wali Khan; Caglar, Murat
In recent years, using the idea of analytic and bi-univalent functions, many ideas have been developed by different well-known authors, but the using Gegenbauer polynomials along with certain bi-univalent functions is very rare in the literature. We are essentially motivated by this recent research going on, here in our present investigation, we make use of certain q-derivative operator and Gegenbauer polynomials and define a new subclass of analytic and bi-univalent functions. We then obtain certain coefficient bounds, the Fekete-Szego inequalities and upper bounds for the second-order Hankel determinant for the defined functions class.
Coefficient Bounds for Q-Starlike Functions Associated with Q-Bernoulli Numbers
(Wilmington Scientific Publisher, LLC, 2023) Caglar, Murat; Orhan, Halit; Srivastava, Hari Mohan
This paper's main goal is to introduce and study a subclass S*(b, q) of q-starlike functions in the unit disk defined by the q-Bernoulli numbers. We determine the coefficient bounds, the upper bounds for the Fekete-Szego functional, and the second Hankel determinant for this subclass.
Coefficient Inequality for a Novel Bi-Univalent Function Subclass Associated with Krawtchouk Polynomials
(Univ Nis, Fac Sci Math, 2025) Orhan, Halit; Caglar, Murat; Arikan, Hava
In this research, we present and study a new subclass of bi-univalent functions related to the Krawtchouk polynomials that meet subordination requirements seen in the open unit disk, a symmetric domain. We derive estimates for the Fekete-Szegoinequality |a(3)-gamma a(2)(2)| and the Taylor-Maclaurin coeffcients |a(2)| , |a(3)| for this new subclass.
Fekete-Szego Inequalities for a New Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials
(MDPI, 2022) Caglar, Murat; Cotirla, Luminita-Ioana; Buyankara, Mucahit
We introduce and investigate in this paper a new subclass of bi-univalent functions associated with the Gegenbauer polynomials which satisfy subordination conditions defined in a symmetric domain, which is the open unit disc. For this new subclass, we obtain estimates for the Taylor-Maclaurin coefficients vertical bar a(2)vertical bar, vertical bar a(3)vertical bar and the Fekete-Szego inequality vertical bar a(3)-mu a(2)(2)vertical bar.
Fekete-Szegö Inequality for a Subclass of Bi-Univalent Functions Linked to Q-Ultraspherical Polynomials
(Universal Wiser Publisher, 2024) Alsoboh, Abdullah; Caglar, Murat; Buyankara, Mucahit
In this study, we introduce a new class of bi-univalent functions using q-Ultraspherical polynomials. We derive the Fekete and Szeg & ouml; functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients | alpha 2 | and | alpha 3 | . Furthermore, a collection of fresh outcomes is presented by customizing the parameters employed in our initial discoveries.
Fekete-Szego Problem for a Subclass of Analytic Functions Associated with Chebyshev Polynomials
(Soc Paranaense Matemática, 2022) Caglar, Murat; Orhan, Halit; Kamali, Muhammet
In this paper, we obtain initial coefficients vertical bar a(2)vertical bar and vertical bar a(3)vertical bar for a certain subclass by means of Chebyshev polynomials expansions of analytic functions in D. Also, we solve Fekete-Szego problem for functions in this subclass.
The Fekete-Szego Problems for Subclass of Bi-Univalent Functions Associated with Sigmoid Function
(Univ Nis, 2022) Orhan, Halit; Murugusundaramoorthy, Gangadharan; Caglar, Murat
The purpose of this article is to introduce a new subclass of analytic and bi-univalent functions, in associated with sigmoid function and to investigate the upper bounds for |a(2)| and |a(3)|, where a(2), a(3) are the initial Taylor-Maclaurin coefficients. Further, we obtain the Fekete-Szego 5 inequalities for this subclass of the bi-univalent function class sigma. We also give several illustrative examples of the bi-univalent function class which we introduce here.
Generalized Coefficient Estimates for a New Subclass of Analytic Functions
(World Scientific Publ Co Pte Ltd, 2025) Orhan, Halit; Caglar, Murat
In this study, a new subclass of analytic functions in the open unit disk was defined with the help of the function obtained by applying the Salagean derivative to the q-Ruscheweyh derivative operator. For the functions belonging to this subclass, the coefficient bounds for the Fekete-Szeg & ouml; functional were determined. The results of this paper are a generalization of the results of Kanas and Darwish [Fekete-Szeg & ouml; problem for starlike and convex functions of complex order, Appl. Math. Lett. 23(7) (2010) 777-782].
The Hardy Space of Ramanujan-Type Entire Functions
(Honam Mathematical Soc, 2023) Deniz, Erhan; Caglar, Murat
In this paper, we deal with some geometric properties in-cluding starlikeness and convexity of order beta of Ramanujan-type entire functions which are natural extensions of classical Ramanujan entire func-tions. In addition, we determine some conditions on the parameters such that the Ramanujan-type entire functions belong to the Hardy space and to the class of bounded analytic functions.
Hermitian-Toeplitz and Hankel Determinants for Sakaguchi-Type Functions Defined by a Rational Function
(Springer, 2025) Buyankara, Mucahit; Caglar, Murat
We obtain the best possible estimates for the Hermitian - Toeplitz determinant of the third order for a class of starlike functions with respect to a symmetric point associated with a rational function. In addition, we determine the upper bounds for the third Hankel determinants.
Inequalities on a Class of Analytic Functions Defined by Generalized Mittag-Leffler Function
(Univ Nis, Fac Sci Math, 2023) Caglar, Murat; Karthikeyan, K. R.; Murugusundaramoorthy, G.
By making use of the generalized difference operator, we have defined a new class of A-pseudo Pascu type functions of complex order using subordination. Interesting results such as subordination re-sults, inequalities for the initial Taylor-Maclaurin coefficients and unified solution of Fekete-Szego problem have been obtained. Also, the study has been extended to quantum calculus by replacing the ordinary derivative with a q-derivative in the defined function class. Several applications, known or new of the main results are also presented.
The Monotony of the Q-Struve Functions
(Springer, 2025) Ozkan, Yucel; Korkmaz, Semra; Deniz, Erhan; Caglar, Murat
In this paper, we prove monotonicity properties for the four different kinds of normalized q-Struve-Bessel functions using the method of subordination factor sequences. In addition, several inequalities related to the q-gamma function have been established. To support the main fundings, graphs derived from specific parameter values were presented. Additionality, in the special case of q -> 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$q\rightarrow 1$\end{document}, we obtain the results of Deniz and Sz & aacute;sz (Complex Anal. Oper. Theory 18:120, 2004).
Neighborhood Properties of Certain Subclasses of Analytic Functions Defined by Generalized Mittag-Leffler Function
(Editura Bibliotheca-bibliotheca Publ House, 2022) Caglar, Murat; Buyukyurt, Elif Kaya
In this paper, we introduce new subclasses M-lambda,mu(n) (alpha, beta, gamma) and R-lambda,mu(n)(alpha, beta, gamma; nu) of analytic functions in the open unit disk Zl with negative coefficients defined by generalized Mittag-Leffler function. The object of the present paper is to determine coefficient inequalities, inclusion relations and neighborhoods properties for functions f (z) belonging to these subclasses.
New Subclasses of Bi-Univalent Functions with Respect to the Symmetric Points Defined by Bernoulli Polynomials
(MDPI, 2022) Buyankara, Mucahit; Caglar, Murat; Cotirla, Luminita-Ioana
In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U = {z is an element of C: |z| < 1} defined by Bernoulli polynomials. We obtain ?? upper bounds for Taylor-Maclaurin coefficients |a(2)|, |a(3)| and Fekete-Szego inequalities a(3) - mu a(2)2 for these new subclasses.
(P, Q)-Lucas Polynomial Coefficient Relations of Bi-Univalent Functions Defined by the Combination of Opoola and Babalola Differential Operators
(Springer Heidelberg, 2022) Orhan, Halit; Shaba, Timilehin Gideon; Caglar, Murat
In the discipline of geometric function theory, Lucas polynomials and other special polynomials have recently acquired traction. We establish a new class of bi-univalent functions and get coefficient estimates and Fekete-Szego inequalities for this new class in this paper by connecting these polynomials, subordination and combination of Babalola and Opoola operator.
Second Hankel Determinant for a Certain Subclass of Analytic Functions Defined by Hypergeometric Functions
(Springer Heidelberg, 2023) Orhan, Halit; Caglar, Murat; Arikan, Hava
In the present paper, we obtain the upper bounds for the second Hankel determinant and Fekete-Szego inequalities for a new subclass of analytic functions in the open unit disk defined by the hypergeometric functions. Moreover, several interesting applications of the results presented here are also discussed.
Second Hankel Determinant for Certain Subclasses of Bi-Starlike Functions Defined by Differential Operators
(Univ Maragheh, 2023) Orhan, Halit; Arikan, Hava; Caglar, Murat
In this paper, we obtain upper bounds of the initial Taylor-Maclaurin coefficients |a2|, |a3| and |a4| and of the Fekete-Szego functional vertical bar a3 - eta a(2) (2)vertical bar for certain subclasses of analytic and 2 bi-starlike functions S sigma*(beta,theta, n, m) in the open unit disk. We have also obtained an upper bound of the functional vertical bar a(2)a(4) - a(2) vertical bar for the 3 functions in the class S sigma*(beta,theta, n, m). Moreover, several interesting applications of the results presented here are also discussed.
Third Hankel Determinant for a Subfamily of Holomorphic Functions Related with Lemniscate of Bernoulli
(MDPI, 2023) Orhan, Halit; Caglar, Murat; Cotirla, Luminita-Ioana
The main goal of this investigation is to obtain sharp upper bounds for Fekete-Szego functional and the third Hankel determinant for a certain subclass SL*(u, v, alpha) of holomorphic functions defined by the Carlson-Shaffer operator in the unit disk. Finally, for some special values of parameters, several corollaries were presented.
Toeplitz Determinants for Λ- Pseudo-Starlike Functions
(Korean Mathematical Soc, 2024) Caglar, Murat; Ibrahim, Ismaila O.; Shaba, Timilehin Gideon; Wanas, Abbas Kareem
. In this article, by making use of the )-pseudo-starlike functions, we introduce a certain family of normalized analytic functions in the open unit disk U and we establish coefficient estimates for the first four determinants of the Toeplitz matrices T2(2), T2(3), T3(2) and T3(1) for the functions belonging to this family. Further, some known and new results which follow as special cases of our results are also mentioned.