Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 7 Sayı: 1, 25 - 32, 15.04.2019

Öz

Kaynakça

  • [1] C. R. Adams, On the linear partial q-difference equation of general type, Trans. Amer. Math. Soc., 31 (1929), 360–371.
  • [2] G. E. Andrews, G. E. Askey and R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999.
  • [3] H. Airault, Remarks on Faber polynomials, Int. Math. Forum., 3 (9–12) (2008), 449–456.
  • [4] H. Airault, A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math., 130 (3) (2006), 179–222.
  • [5] H. Airault, J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., 126 (5) (2002), 343–367.
  • [6] H. Airault. Symmetric sums associated to the factorizations of Grunsky coefficients, in: Conference, Groups and Symmetries Montreal Canada, April 2007.
  • [7] R. M. Ali, S. K. Lee, V. Ravichandran, S. Supramaniam, Coefficient estimates for bi-univalent Ma–Minda starlike and convex functions, Appl. Math. Lett., 25 (3) (2012), 344–351.
  • [8] Ş. Altınkaya, S. Yalçın, Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces, (2015), 145242, 5 pp.
  • [9] Ş . Altınkaya, S. Yalçın, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Acta Univ. Apulensis, Mat. Inform., 40 (2014), 347–354.
  • [10] Ş. Altınkaya, S. Yalçın, Initial coefficient bounds for a general class of bi-univalent functions, Int. J. Anal., (2014), 867871, 4 pp.
  • [11] Ş. Altınkaya, S. Yalçın, Faber polynomial coefficient bounds for a subclass of bi-univalent functions. C. R. Acad. Sci. Paris Ser. I, 353 (2015), 1075-1080.
  • [12] D. A. Brannan, J. Clunie, Aspects of contemporary complex analysis, Proceedings of the NATO Advanced Study Instute Held at University of Durham, New York, Academic Press, 1979.
  • [13] S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris Ser. I, 352 (6) (2014), 479–484.
  • [14] R. D. Carmichael, The general theory of linear q-difference equations, Amer. J. Math., 34 (1912), 147–168.
  • [15] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983.
  • [16] G. Faber, Uber polynomische Entwickelungen, Math. Ann., 57 (3) (1903), 389–408.
  • [17] B. A. Frasin, M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (9) (2011), 1569–1573.
  • [18] M. Govindaraj, S. Sivasubramanian, On a class of analytic functions related to conic domains involving q-calculus, Analysis Math., 43 (3) (2017), 475-487.
  • [19] H. Grunsky, Koffizientenbedingungen fur schlict abbildende meromorphe funktionen, Math. Zeit., 45 (1939), 29-61.
  • [20] S. G. Hamidi, J. M. Jahangiri, Faber polynomial coefficient estimates for analytic bi-close-to-convex functions, C. R. Acad. Sci. Paris Ser. I, 352 (1) (2014), 17–20.
  • [21] S. G. Hamidi, J. M. Jahangiri, Faber polynomial coefficients of bi-subordinate functions, C. R. Acad. Sci. Paris Ser. I, 354 (2016), 365–370.
  • [22] S. G. Hamidi, J.M. Jahangiri, Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations, Bull. Iran. Math. Soc., 41 (5) (2015), 1103–1119.
  • [23] S. Hussain, S. Khan, M. A. Zaighum, Maslina Darus, and Zahid Shareef, Coefficients Bounds for Certain Subclass of Biunivalent Functions Associated with Ruscheweyh q-Differential Operator, Journal of Complex Analysis, (2017), 2826514, 9 pp.
  • [24] M. E. H. Ismail, E. Merkes and D. Styer, A generalization of starlike functions, Complex Variables Theory Appl., 14 (1990), 77–84.
  • [25] F. H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math., 41 (15) (1910), 193–203.
  • [26] J. M. Jahangiri, On the coefficients of powers of a class of Bazilevic functions, Indian J. Pure Appl. Math., 17 (9) (1986), 1140–1144.
  • [27] J. M. Jahangiri, S.G. Hamidi, Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci. (2013), 190560, 4 pp.
  • [28] J. M. Jahangiri, S.G. Hamidi, S. Abd Halim, Coefficients of bi-univalent functions with positive real part derivatives, Bull. Malays. Math. Soc., (2) 3 (2014), 633–640.
  • [29] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), 63-68.
  • [30] T. E. Mason, On properties of the solution of linear q-difference equations with entire function coefficients, Amer. J. Math., 37 (1915), 439–444.
  • [31] E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in jzj < 1, Archive for Rational Mechanics and Analysis, 32 (1969), 100-112.
  • [32] G. S. Salagean, Subclasses of univalent functions, in: Complex Analysis, fifth Romanian–Finnish Seminar, Part 1 (Bucharest, 1981), Lecture Notes in Mathematics, 1013, Springer (Berlin, 1983), 362–372.
  • [33] M. Schiffer, A method of variation within the family of simple functions, Proc. London Math. Soc., 44 (1938), 432-449.
  • [34] A. C. Schaeffer, D. C. Spencer, The coefficients of schlict functions, Duke Math. J., 10 (1943), 611-635
  • [35] H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (10) (2010), 1188–1192.
  • [36] H. M. Srivastava, S. S. Eker, R. M. Ali, Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29 (8) (2015), 1839–1845.
  • [37] W. J. Trjitzinsky, Analytic theory of linear q-difference equations, Acta Math., 61 (1933), 1–38.
  • [38] P. G. Todorov, On the Faber polynomials of the univalent functions of class , J. Math. Anal. Appl., 162 (1) (1991), 268-276.

Faber Polynomial Coefficients Estimates of Bi-univalent Functions Associated with Generalized Salagean q-Differential Operator

Yıl 2019, Cilt: 7 Sayı: 1, 25 - 32, 15.04.2019

Öz

In this paper, we introduce a new subclass of analytic and bi-univalent functions by using generalized Salagean $q$-differential operator in open unit disc $E=\left \{ z:z\in \mathbb{C} \text{ and }\left \vert z\right \vert <1\right \} $. By using Faber polynomial expansions and $q-$analysis to find a general coefficient bounds $|a_{n}|,$ for $n\geq 3,$ of class of bi-subordinate functions, also find initial coefficients bounds$.$ We also highlight some known consequences of our main results.

Kaynakça

  • [1] C. R. Adams, On the linear partial q-difference equation of general type, Trans. Amer. Math. Soc., 31 (1929), 360–371.
  • [2] G. E. Andrews, G. E. Askey and R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999.
  • [3] H. Airault, Remarks on Faber polynomials, Int. Math. Forum., 3 (9–12) (2008), 449–456.
  • [4] H. Airault, A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math., 130 (3) (2006), 179–222.
  • [5] H. Airault, J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., 126 (5) (2002), 343–367.
  • [6] H. Airault. Symmetric sums associated to the factorizations of Grunsky coefficients, in: Conference, Groups and Symmetries Montreal Canada, April 2007.
  • [7] R. M. Ali, S. K. Lee, V. Ravichandran, S. Supramaniam, Coefficient estimates for bi-univalent Ma–Minda starlike and convex functions, Appl. Math. Lett., 25 (3) (2012), 344–351.
  • [8] Ş. Altınkaya, S. Yalçın, Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces, (2015), 145242, 5 pp.
  • [9] Ş . Altınkaya, S. Yalçın, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Acta Univ. Apulensis, Mat. Inform., 40 (2014), 347–354.
  • [10] Ş. Altınkaya, S. Yalçın, Initial coefficient bounds for a general class of bi-univalent functions, Int. J. Anal., (2014), 867871, 4 pp.
  • [11] Ş. Altınkaya, S. Yalçın, Faber polynomial coefficient bounds for a subclass of bi-univalent functions. C. R. Acad. Sci. Paris Ser. I, 353 (2015), 1075-1080.
  • [12] D. A. Brannan, J. Clunie, Aspects of contemporary complex analysis, Proceedings of the NATO Advanced Study Instute Held at University of Durham, New York, Academic Press, 1979.
  • [13] S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris Ser. I, 352 (6) (2014), 479–484.
  • [14] R. D. Carmichael, The general theory of linear q-difference equations, Amer. J. Math., 34 (1912), 147–168.
  • [15] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983.
  • [16] G. Faber, Uber polynomische Entwickelungen, Math. Ann., 57 (3) (1903), 389–408.
  • [17] B. A. Frasin, M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (9) (2011), 1569–1573.
  • [18] M. Govindaraj, S. Sivasubramanian, On a class of analytic functions related to conic domains involving q-calculus, Analysis Math., 43 (3) (2017), 475-487.
  • [19] H. Grunsky, Koffizientenbedingungen fur schlict abbildende meromorphe funktionen, Math. Zeit., 45 (1939), 29-61.
  • [20] S. G. Hamidi, J. M. Jahangiri, Faber polynomial coefficient estimates for analytic bi-close-to-convex functions, C. R. Acad. Sci. Paris Ser. I, 352 (1) (2014), 17–20.
  • [21] S. G. Hamidi, J. M. Jahangiri, Faber polynomial coefficients of bi-subordinate functions, C. R. Acad. Sci. Paris Ser. I, 354 (2016), 365–370.
  • [22] S. G. Hamidi, J.M. Jahangiri, Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations, Bull. Iran. Math. Soc., 41 (5) (2015), 1103–1119.
  • [23] S. Hussain, S. Khan, M. A. Zaighum, Maslina Darus, and Zahid Shareef, Coefficients Bounds for Certain Subclass of Biunivalent Functions Associated with Ruscheweyh q-Differential Operator, Journal of Complex Analysis, (2017), 2826514, 9 pp.
  • [24] M. E. H. Ismail, E. Merkes and D. Styer, A generalization of starlike functions, Complex Variables Theory Appl., 14 (1990), 77–84.
  • [25] F. H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math., 41 (15) (1910), 193–203.
  • [26] J. M. Jahangiri, On the coefficients of powers of a class of Bazilevic functions, Indian J. Pure Appl. Math., 17 (9) (1986), 1140–1144.
  • [27] J. M. Jahangiri, S.G. Hamidi, Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci. (2013), 190560, 4 pp.
  • [28] J. M. Jahangiri, S.G. Hamidi, S. Abd Halim, Coefficients of bi-univalent functions with positive real part derivatives, Bull. Malays. Math. Soc., (2) 3 (2014), 633–640.
  • [29] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), 63-68.
  • [30] T. E. Mason, On properties of the solution of linear q-difference equations with entire function coefficients, Amer. J. Math., 37 (1915), 439–444.
  • [31] E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in jzj < 1, Archive for Rational Mechanics and Analysis, 32 (1969), 100-112.
  • [32] G. S. Salagean, Subclasses of univalent functions, in: Complex Analysis, fifth Romanian–Finnish Seminar, Part 1 (Bucharest, 1981), Lecture Notes in Mathematics, 1013, Springer (Berlin, 1983), 362–372.
  • [33] M. Schiffer, A method of variation within the family of simple functions, Proc. London Math. Soc., 44 (1938), 432-449.
  • [34] A. C. Schaeffer, D. C. Spencer, The coefficients of schlict functions, Duke Math. J., 10 (1943), 611-635
  • [35] H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (10) (2010), 1188–1192.
  • [36] H. M. Srivastava, S. S. Eker, R. M. Ali, Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29 (8) (2015), 1839–1845.
  • [37] W. J. Trjitzinsky, Analytic theory of linear q-difference equations, Acta Math., 61 (1933), 1–38.
  • [38] P. G. Todorov, On the Faber polynomials of the univalent functions of class , J. Math. Anal. Appl., 162 (1) (1991), 268-276.
Toplam 38 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Sibel Yalçın

Shahid Khan Bu kişi benim

Saqib Hussain

Yayımlanma Tarihi 15 Nisan 2019
Gönderilme Tarihi 22 Ocak 2019
Kabul Tarihi 4 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 1

Kaynak Göster

APA Yalçın, S., Khan, S., & Hussain, S. (2019). Faber Polynomial Coefficients Estimates of Bi-univalent Functions Associated with Generalized Salagean q-Differential Operator. Konuralp Journal of Mathematics, 7(1), 25-32.
AMA Yalçın S, Khan S, Hussain S. Faber Polynomial Coefficients Estimates of Bi-univalent Functions Associated with Generalized Salagean q-Differential Operator. Konuralp J. Math. Nisan 2019;7(1):25-32.
Chicago Yalçın, Sibel, Shahid Khan, ve Saqib Hussain. “Faber Polynomial Coefficients Estimates of Bi-Univalent Functions Associated With Generalized Salagean Q-Differential Operator”. Konuralp Journal of Mathematics 7, sy. 1 (Nisan 2019): 25-32.
EndNote Yalçın S, Khan S, Hussain S (01 Nisan 2019) Faber Polynomial Coefficients Estimates of Bi-univalent Functions Associated with Generalized Salagean q-Differential Operator. Konuralp Journal of Mathematics 7 1 25–32.
IEEE S. Yalçın, S. Khan, ve S. Hussain, “Faber Polynomial Coefficients Estimates of Bi-univalent Functions Associated with Generalized Salagean q-Differential Operator”, Konuralp J. Math., c. 7, sy. 1, ss. 25–32, 2019.
ISNAD Yalçın, Sibel vd. “Faber Polynomial Coefficients Estimates of Bi-Univalent Functions Associated With Generalized Salagean Q-Differential Operator”. Konuralp Journal of Mathematics 7/1 (Nisan 2019), 25-32.
JAMA Yalçın S, Khan S, Hussain S. Faber Polynomial Coefficients Estimates of Bi-univalent Functions Associated with Generalized Salagean q-Differential Operator. Konuralp J. Math. 2019;7:25–32.
MLA Yalçın, Sibel vd. “Faber Polynomial Coefficients Estimates of Bi-Univalent Functions Associated With Generalized Salagean Q-Differential Operator”. Konuralp Journal of Mathematics, c. 7, sy. 1, 2019, ss. 25-32.
Vancouver Yalçın S, Khan S, Hussain S. Faber Polynomial Coefficients Estimates of Bi-univalent Functions Associated with Generalized Salagean q-Differential Operator. Konuralp J. Math. 2019;7(1):25-32.
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