Browsing by Author "ALTINKAYA, ŞAHSENE"
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Publication A new class of salagean-type multivalent harmonic functions defined by subordination(Springer Int Publ Ag, 2020-10-18) Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Çakmak, Serkan; Yalçın, Sibel; YALÇIN TOKGÖZ, SİBEL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/MatematikAnabilim Dalı.; 0000-0002-0243-8263; 0000-0002-7950-8450; GZG-2072-2022; AAA-8330-2021; AAE-9745-2020Utilizing the concepts of subordination we have introduced a generalized class Salagean-Type of complex-valued multivalent harmonic functions. We construct some properties of our class. The results obtained here include a number of known and new results as their special cases.Publication A subclass of analytic functions defined by using mittag-leffler function(Honam Mathematical Soc, 2020-09-01) Mahmood, Tahir; Naeem, Muhammad; Hussain, Saqib; Khan, Shahid; Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/ Matematik Bölümü.; 0000-0002-7950-8450; AAA-8330-2021In this paper, new subclasses of analytic functions are proposed by using Mittag-Leffler function. Also some properties of these classes are studied in regard to coefficient inequality, distortion theorems, extreme points, radii of starlikeness and convexity and obtained numerous sharp results.Publication A subclass of bi-univalent functions based on the faber polynomial expansions and the fibonacci numbers(Mdpi, 2019-02-01) Altınkaya, Şahsene; Yalçın, Sibel; Çakmak, Serkan; ALTINKAYA, ŞAHSENE; YALÇIN TOKGÖZ, SİBEL; Çakmak, Serkan; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; 0000-0002-0243-8263; 0000-0003-0368-7672; AAE-9745-2020; ABC-6175-2020; GZG-2072-2022; AAA-8330-2021In this investigation, by using the Komatu integral operator, we introduce the new class ( pound eta,rho)(Sigma,t)((rho) over tilde of bi-univalent functions based on the rule of subordination. Moreover, we use the Faber polynomial expansions and Fibonacci numbers to derive bounds for the general coefficient vertical bar a(n)vertical bar of the bi-univalent function class.Publication Application of quasi-subordination for generalized sakaguchi type functions(Hindawi, 2017-01-01) Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; AAA-8330-2021The author constructs a new class S-q(lambda)(G, s, l) of univalent functions applying the Ruscheweyh derivative. Moreover, the coefficient estimates including a Fekete-Szego inequality of this class were determined.Publication Certain classes of bi-univalent functions of complex order associated with quasi-subordination involving (p, q)-derivative operator(Univ Kragujevac, Fac Science, 2020-01-01) Altınkaya, Şahsene; Yalçın Sibel; ALTINKAYA, ŞAHSENE; YALÇIN TOKGÖZ, SİBEL; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; 0000-0002-0243-8263; AAE-9745-2020; AAA-8330-2021In this present paper, as applications of the post-quantum calculus known as the (p, q)-calculus, we construct a new class D-p,q(k) (gamma, zeta, Psi) of bi-univalent functions of complex order defined in the open unit disk. Coefficients inequalities and several special consequences of the results are obtained.Publication Certain subclasses of bi-univalent functions associated with the horadam polynomials(Springer, 2019-08-01) Srivastava, H. M.; Altınkaya, Şahsene; Yalçın, Sibel; ALTINKAYA, ŞAHSENE; YALÇIN TOKGÖZ, SİBEL; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; 0000-0002-0243-8263; AAA-8330-2021; ABC-6175-2020; AAE-9745-2020In Geometric Function Theory, there have been many interesting and fruitful usages of a wide variety of special functions and special polynomials. Here, in this article, we propose to make use of the Horadam polynomials which are known to include, as their particular cases, such potentially useful polynomials as (for example) the Fibonacci polynomials, the Lucas polynomials, the Pell polynomials, the Pell-Lucas polynomials, and the Chebyshev polynomials of the second kind. We aim first at introducing a new class of bi-univalent functions defined by means of the Horadam polynomials. For functions belonging to this new bi-univalent function class, we then derive coefficient inequalities and consider the celebrated Fekete-Szego problem. We also provide relevant connections of our results with those considered in earlier investigations.Publication Certain subclasses of harmonic univalent functions defined by subordination(Southeast Asian Mathematical Soc-seams, 2020-01-01) Çakmak, Serkan; Yalçın, S.; YALÇIN TOKGÖZ, SİBEL; Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0243-8263; 0000-0002-7950-8450; GZG-2072-2022; AAA-8330-2021; AAE-9745-2020In this article, we consider some results involving the modified Salagean operator. We give coefficient bounds for these subclasses. Moreover, we discuss necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for these subclasses of functions.Publication Coefficient estimates and fekete-szego inequality for a class of analytic functions satisfying subordinate condition associated with chebyshev polynomials(Sciendo, 2019-12-01) Szatmari, Eszter; Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-7950-8450; AAA-8330-2021In this paper, we define a class of analytic functions, F(H, alpha, delta, mu), satisfying the following condition(alpha[zf'(z)/f(z)](delta) + (1-alpha) [zf'(z)/f(z)](mu)[1+zf ''(z)/f'(z)](1-mu)) (sic) H(z, t),where alpha is an element of [0, 1], delta is an element of [1, 2] and mu is an element of [0, 1].We give coefficient estimates and Fekete-Szego inequality for this class.Publication Faber polynomial coefficient bounds for a subclass of bi-univalent functions(Elsevier, 2015-12-01) Altınkaya, Şahsene; Yalçın, Sibel; ALTINKAYA, ŞAHSENE; YALÇIN TOKGÖZ, SİBEL; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; 0000-0002-0243-8263; AAA-8330-2021; AAE-9745-2020; ABC-6175-2020In this work, considering a general subclass of bi-univalent functions and using the Faber polynomials, we obtain coefficient expansions for functions in this class. In certain cases, our estimates improve some of those existing coefficient bounds.Publication Functions of bounded variation related to domains bounded by conic sections(Walter, 2019-08-01) Kanas, Stanislawa; Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; AAA-8330-2021The aim of this paper is to bring together two areas of studies in the theory of analytic functions: functions of bounded variation and functions related to domains bounded by conic sections. Some relevant properties are indicated.Publication Generalized distribution associated with quasi-subordination in terms of error function and bell numbers(Yarmouk Univ, Deanship Research & Graduate Studies, 2021-03-01) Olatunji, Sunday Oluwafemi; Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi; 0000-0002-7950-8450; FZT-6434-2022Generalized distribution is a statistical tools used in geometric function theory in recent time because of its application to real life problems. In this present work, the generalized distribution associated with quasi-subordination in terms of error function and bell numbers were studied. The first few coefficient bounds were obtained which are used to obtain the Fekete-Szego inequality.Publication Generalized distribution for analytic function classes associated with error functions and Bell numbers(Springer, 2019-10-24) Altınkaya, Şahsene; Olatunji, Sunday Oluwafemi; ALTINKAYA, ŞAHSENE; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-7950-8450; AAA-8330-2021The primary motivation of the paper is to study the generalized distribution for analytic function classes associated with error functions and Bell numbers. Further, the authors estimate the bounds for probability distribution series by means of q-difference operator using subordination principle.Publication Generalized hankel determinant for a general subclass of univalent functions(Turkic World Mathematical Soc, 2018-01-01) Yalçın, Sibel; Altınkaya, Şahsene; Owa, S.; YALÇIN TOKGÖZ, SİBEL; ALTINKAYA, ŞAHSENE; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0243-8263; AAE-9745-2020; AAA-8330-2021Making use of the generalized Hankel determinant, in this work, we consider a general subclass of univalent functions. Moreover, upper bounds are obtained for vertical bar a(3) - mu a(2)(2)vertical bar, where mu is an element of R.Publication Inclusion properties of Lucas polynomials for bi-univalent functions introduced through the q-analogue of the noor integral operator(Tübitak Bilimsel ve Teknolojik Araştırma Kurumu, 2019-01-01) Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; AAA-8330-2021In this paper, by using the (P, Q)-Lucas polynomials and the q-analogue of the Noor integral operator, we aim to build a bridge between the theory of geometric functions and that of special functions.Publication Initial coefficient bounds for a general class of biunivalent functions(Hindawi, 2014-01-01) Altınkaya, Şahsene; Yalçın, Sibel; ALTINKAYA, ŞAHSENE; YALÇIN TOKGÖZ, SİBEL; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; 0000-0002-0243-8263; AAE-9745-2020; AAA-8330-2021We find estimates on the coefficients vertical bar a2 vertical bar and vertical bar a3 vertical bar for functions in the function class B (lambda,mu,phi)). The results presented in this paper improve or generalize the recent work of Srutha Keerthi and Raja (2013)Publication On a new class of analytic functions related to fractional calculus(Publ House Bulgarian Acad Sci, 2020-01-01) Owa, Shigeyoshi; Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Yalçın, Sibel; YALÇIN TOKGÖZ, SİBEL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi.; 0000-0002-7950-8450; 0000-0002-0243-8263; AAA-8330-2021; AAE-9745-2020Let A be the class of analytic functions f with f(0) = 0 and f'(0) = 1 in the open unit disk U. Applying the fractional derivative D-z(lambda) f of order lambda for f is an element of A, a new subclass A(alpha, beta; lambda) of A with 0 <= alpha < 1, beta > 1 and 0 <= lambda < 1 is considered. The object of the present paper is to discuss some interesting properties of this class of functions.Publication On a new subclass of bi-univalent functions satisfying subordinate conditions(Ankara Üniversitesi, 2019-01-01) Mazi, Emeka; Altınkaya, Şahsene; ALTINKAYA, ŞAHSENE; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; AAA-8330-2021The purpose of our present paper is to introduce a new subclass of bi-univalent functions associated with pseudo-starlike function with Sakaguchi type functions and to determine the coefficient estimates vertical bar a(2)vertical bar and vertical bar a(3)vertical bar for functions in each of this newly-defined class. We also highlight some known consequences of our main results.Publication On salagean type pseudo-starlike functions(Univ Tartu Press, 2017-12-01) Altinkaya, Sahsene; Özkan, Yeşim Sağlam; ALTINKAYA, ŞAHSENE; SAĞLAM ÖZKAN, YEŞİM; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; 0000-0002-1364-5137; AAA-8330-2021; G-5333-2017We construct two new subclasses of univalent functions in the open unit disk U = {z : vertical bar z vertical bar < 1 . For the first class ( pound lambda)(beta) of Salagean type lambda--pseudo-starlike functions, using the sigmoid function, we establish upper bounds for the initial coefficients of the functions in this class. Furthermore, for the second class ( pound lambda)(beta, phi) we obtain Fekete-Szego inequalities. The results presented in this paper generalize the recent work of Babalola.Publication On some subclasses of M fold symmetric bi-univalent functions(Ankara Üniversitesi, 2018-01-01) Altınkaya, Şahsene; Yalçın, Sibel; ALTINKAYA, ŞAHSENE; YALÇIN TOKGÖZ, SİBEL; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; 0000-0002-0243-8263; AAE-9745-2020; ABC-6175-2020; AAA-8330-2021In this work, we introduce two new subclasses S-Sigma m (alpha, lambda) and S-Sigma m (beta, lambda) of Sigma(m) consisting of analytic and m -fold symmetric bi-univalent functions in the open unit disc U. Furthermore, for functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for vertical bar a(m)+1 vertical bar and alpha(2m)+1 vertical bar.Publication On the chebyshev polynomial coefficient problem of bi-bazilevi functions(Türk Dünyası Matematik Topluluğu, 2020-01-01) AltInkaya, Şahsene; Yalçın, Sibel; ALTINKAYA, ŞAHSENE; YALÇIN TOKGÖZ, SİBEL; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7950-8450; 0000-0002-0243-8263; AAA-8330-2021; ABC-6175-2020; AAE-9745-2020A function said to be bi-Bazilevic in the open unit disk U if both the function and its inverse are Bazilevic there. In this paper, we will study a newly constructed class of bi-Bazilevic functions. Furthermore, we establish Chebyshev polynomial bounds for the coefficients, and get Fekete-Szego inequality, for the class B(beta, t).