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Coefficients estimates of a new class of analytic bi-univalent functions with bounded boundary rotation

Year 2022, Volume: 51 Issue: 5, 1271 - 1279, 01.10.2022

Pranay Goswami Serap Bulut Neetu Sekhawat

https://doi.org/10.15672/hujms.822815
Cited By: 1

Abstract

In this paper, we introduce a new subclass of analytic bi-univalent functions defined by using $q$-derivative operator. Further, we obtain both some initial and general coefficient bounds, and also Fekete-Szegö inequalities for bi-univalent functions that belong to this class. Our results extend and improve some known results as special cases.

Keywords

univalent functions bi-univalent functions bounded boundary rotations coefficient estimates fekete-Szegö problem q-calculus

References

  • [1] H. Airault, Symmetric sums associated to the factorization of Grunsky coefficients, in Conference, Groups and Symmetries, Montreal, Canada, April 2007.
  • [2] H. Airault, Remarks on Faber polynomials, Int. Math. Forum 3(9-12), 449–456, 2008.
  • [3] H. Airault and A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math. 20(3), 179–222, 2006.
  • [4] R.M. Ali, S.K. Lee, V. Ravichandran and S. Supramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25(3), 344–351, 2012.
  • [5] A. Aljouiee and P. Goswami, Coefficients estimates of the class of bi-univalent functions, J. Function Spaces 2016, Article ID 3454763, 4 pages, 2016.
  • [6] D.A. Brannan and T.S. Taha, On some classes of bi-univalent functions, Studia Univ. Babeş-Bolyai Math. 31(2), 70–77, 1986.
  • [7] P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, 259, Springer, New York, 1983.
  • [8] G. Faber, Über polynomische Entwickelungen, Math. Ann. 57 (3), 389–408, 1903.
  • [9] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24(9), 1569–1573, 2011.
  • [10] S.P. Goyal and P. Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc. 20(3), 179–182, 2012.
  • [11] S.G. Hamidi, S.A. Halim and J.M. Jahangiri, Coefficient of bi-univalent functions with positive real parts, Bull. Malaysian Math. Sci. Soc. 37(3), 633–640, 2014.
  • [12] F.H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math. 41, 193–203, 1910.
  • [13] F.H. Jackson, q-difference equations, Amer. J. Math. 32, 305–314, 1910.
  • [14] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18, 63–68, 1967.
  • [15] K. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math. 31, 311–323, 1975.
  • [16] B. Pinchuk, Functions with bounded boundary rotation, Israel J. Math. 10, 7–16, 1971.
  • [17] M. Schiffer, Faber polynomials in the theory of univalent functions, Bull. Amer. Math. Soc. 54, 503–517, 1948.
  • [18] P.G. Todorov, On the Faber polynomials of the univalent functions of class $\Sigma$, J. Math. Anal. Appl. 162(1), 268-267, 1991.
  • [19] H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23(10), 1188–1192, 2010.
  • [20] P. Zaprawa, Estimates of initial coefficients for bi-univalent functions, Abstr. Appl. Anal. Art. ID 357480, 6 pp. 2014.
  • [21] P. Zaprawa, On the Fekete-Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21(1), 169–178, 2014.

Year 2022, Volume: 51 Issue: 5, 1271 - 1279, 01.10.2022

Pranay Goswami Serap Bulut Neetu Sekhawat

https://doi.org/10.15672/hujms.822815
Cited By: 1

Abstract

References

  • [1] H. Airault, Symmetric sums associated to the factorization of Grunsky coefficients, in Conference, Groups and Symmetries, Montreal, Canada, April 2007.
  • [2] H. Airault, Remarks on Faber polynomials, Int. Math. Forum 3(9-12), 449–456, 2008.
  • [3] H. Airault and A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math. 20(3), 179–222, 2006.
  • [4] R.M. Ali, S.K. Lee, V. Ravichandran and S. Supramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25(3), 344–351, 2012.
  • [5] A. Aljouiee and P. Goswami, Coefficients estimates of the class of bi-univalent functions, J. Function Spaces 2016, Article ID 3454763, 4 pages, 2016.
  • [6] D.A. Brannan and T.S. Taha, On some classes of bi-univalent functions, Studia Univ. Babeş-Bolyai Math. 31(2), 70–77, 1986.
  • [7] P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, 259, Springer, New York, 1983.
  • [8] G. Faber, Über polynomische Entwickelungen, Math. Ann. 57 (3), 389–408, 1903.
  • [9] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24(9), 1569–1573, 2011.
  • [10] S.P. Goyal and P. Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc. 20(3), 179–182, 2012.
  • [11] S.G. Hamidi, S.A. Halim and J.M. Jahangiri, Coefficient of bi-univalent functions with positive real parts, Bull. Malaysian Math. Sci. Soc. 37(3), 633–640, 2014.
  • [12] F.H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math. 41, 193–203, 1910.
  • [13] F.H. Jackson, q-difference equations, Amer. J. Math. 32, 305–314, 1910.
  • [14] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18, 63–68, 1967.
  • [15] K. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math. 31, 311–323, 1975.
  • [16] B. Pinchuk, Functions with bounded boundary rotation, Israel J. Math. 10, 7–16, 1971.
  • [17] M. Schiffer, Faber polynomials in the theory of univalent functions, Bull. Amer. Math. Soc. 54, 503–517, 1948.
  • [18] P.G. Todorov, On the Faber polynomials of the univalent functions of class $\Sigma$, J. Math. Anal. Appl. 162(1), 268-267, 1991.
  • [19] H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23(10), 1188–1192, 2010.
  • [20] P. Zaprawa, Estimates of initial coefficients for bi-univalent functions, Abstr. Appl. Anal. Art. ID 357480, 6 pp. 2014.
  • [21] P. Zaprawa, On the Fekete-Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21(1), 169–178, 2014.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Pranay Goswami

Serap Bulut 0000-0002-6506-4588

Neetu Sekhawat This is me

Publication Date October 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 5

Cite

APA Goswami, P., Bulut, S., & Sekhawat, N. (2022). Coefficients estimates of a new class of analytic bi-univalent functions with bounded boundary rotation. Hacettepe Journal of Mathematics and Statistics, 51(5), 1271-1279. https://doi.org/10.15672/hujms.822815
AMA Goswami P, Bulut S, Sekhawat N. Coefficients estimates of a new class of analytic bi-univalent functions with bounded boundary rotation. Hacettepe Journal of Mathematics and Statistics. October 2022;51(5):1271-1279. doi:10.15672/hujms.822815
Chicago Goswami, Pranay, Serap Bulut, and Neetu Sekhawat. “Coefficients Estimates of a New Class of Analytic Bi-Univalent Functions With Bounded Boundary Rotation”. Hacettepe Journal of Mathematics and Statistics 51, no. 5 (October 2022): 1271-79. https://doi.org/10.15672/hujms.822815.
EndNote Goswami P, Bulut S, Sekhawat N (October 1, 2022) Coefficients estimates of a new class of analytic bi-univalent functions with bounded boundary rotation. Hacettepe Journal of Mathematics and Statistics 51 5 1271–1279.
IEEE P. Goswami, S. Bulut, and N. Sekhawat, “Coefficients estimates of a new class of analytic bi-univalent functions with bounded boundary rotation”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 5, pp. 1271–1279, 2022, doi: 10.15672/hujms.822815.
ISNAD Goswami, Pranay et al. “Coefficients Estimates of a New Class of Analytic Bi-Univalent Functions With Bounded Boundary Rotation”. Hacettepe Journal of Mathematics and Statistics 51/5 (October 2022), 1271-1279. https://doi.org/10.15672/hujms.822815.
JAMA Goswami P, Bulut S, Sekhawat N. Coefficients estimates of a new class of analytic bi-univalent functions with bounded boundary rotation. Hacettepe Journal of Mathematics and Statistics. 2022;51:1271–1279.
MLA Goswami, Pranay et al. “Coefficients Estimates of a New Class of Analytic Bi-Univalent Functions With Bounded Boundary Rotation”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 5, 2022, pp. 1271-9, doi:10.15672/hujms.822815.
Vancouver Goswami P, Bulut S, Sekhawat N. Coefficients estimates of a new class of analytic bi-univalent functions with bounded boundary rotation. Hacettepe Journal of Mathematics and Statistics. 2022;51(5):1271-9.

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