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Year 2021, Volume: 9 Issue: 1, 137 - 142, 28.04.2021

Timilehin Shaba

Abstract

References

  • [1] A. Akgul, Finding initial coefficients for a class of bi-univalent functions given by q-derivative, AIP Conference Proceedings ,1926, 020001(2018).
  • [2] A. Akgul, On the coefficient estimates of analytic and bi-univalent m-fold symmetric functions, Mathematica Aeterna, 7(3) (1993) 253-260.
  • [3] H. Aldweby and M. Darus, A subclass of harmonic U univalent functions associated with q-analogue of Dziok-Srivastava operator, ISRN Mathematical Analysis, 2013 (2013), Article ID 382312, 6 pages.
  • [4] H. Aldweby and M. Darus, Coefficient estimates for initial taylor-maclaurin coefficients for a subclass of analytic and bi-univalent functions associated with q-derivative operator, Recent Trends in Pure and Applied Mathematics, 2017 (2017).
  • [5] S¸. Altinkaya, S. Yalc¸in, On some subclasses of m-fold symmetric bi-univalent functions, Communications Faculty of Sciences University of Series A1: Mathematics and Statistics, 67(1) (2018) 29-36.
  • [6] A. Aral, V. Gupta and R. P. Agarwal, Application of q-Calculus in Operator Theory, Springer, New York, USA, 2013.
  • [7] D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Universitatis Babes¸-Bolyai, Mathematica, 31(2) (1986) 70-7.
  • [8] S. Bulut, Coefficient estimates for general subclasses of m-fold symmetric analytic bi-univalent functions, Turkish J. Math., 40, (2016) 1386-1397.
  • [9] S. Bulut, Certain subclasses of analytic and bi-univalent functions involving the q-derivative operator, Communications Faculty of Sciences University of Series A1: Mathematics and Statistics, 66(1) (2017) 108-114.
  • [10] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenchaften, Springer, New York, NY, USA, 1983.
  • [11] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (2004), 1529-1573.
  • [12] S.G Hamiidi and J.M. Jahangiri, Unpredictability of the coefficients of m-fold symmetric bi-starlike functions , Internat. J. Math., 25(7), (2014) 1-8.
  • [13] F. H. Jackson , On q-definite integrals, The Quarterly Journal of Pure and Applied Mathematics , 41 (1910), 193-203.
  • [14] F. H. Jackson , On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh , 46 (1908), 253-281.
  • [15] M. Lewin, On a coefficients problem of bi-univalent functions, Proc. Am. Math. Soc., 18 (1967), 63-68.
  • [16] A. Mohammmed, M. Darus, A generalized operator involving the q-hypergeometric function, Mat. Vesnik, 65 (2013), 454-465.
  • [17] F. Muge Sakar, M. O. Guney, Coefficient estimates for certain subclasses of m-mold symmetric bi-univalent functions defined by the q-derivative operator, Konuralp Journal of Mathematics, 6(2) (2018), 279-285.
  • [18] C.H. Pommerenke, Univalent Functions, Vandendoeck and Rupercht, Gottingen, 1975.
  • [19] T. M. Seoudy and M. K. Aouf, Convolution properties for C certain classes of analytic functions defined by q-derivative operator, Abstract and Applied Analysis, 2014 (2014), Article ID 846719, 7 pages.
  • [20] T. M. Seoudy and M. K. Aouf, Coefficient estimates of new classes of q-starlike and q-convex functions of complex order , Journal of Mathematical Inequalities , 10(1) (2016), 135-145.
  • [21] T. G. Shaba, On some new subclass of bi-univalent functions associated with the Opoola differential operator, Open J. Math. Anal., 4 (2), (2020), 74–79.
  • [22] T. G. Shaba, Certain new subclasses of m-fold symmetric bi-pseudo-starlike functions using Q-derivative operator, Open J. Math. Anal., 5 (1), (2021), 42–50.
  • [23] T. G. Shaba, Subclass of bi-univalent functions satisfying subordinate conditions defined by Frasin differential operator, Turkish Journal of Inequalities, 4 (2) (2020), 50–58.
  • [24] T. G. Shaba, On some subclasses of bi-pseudo-starlike functions defined by Salagean differential operator, Asia Pac. J. Math., 8 (6) (2021), 1–11; Available online at https://doi:10.28924/apjm/8-6 .
  • [25] T. G. Shaba, A. B. Patil, Coefficient estimates for certain subclasses of m-fold symmetric bi-univalent functions associated with pseudo-starlike functions, Earthline Journal of Mathematical Sciences, 6 (2) (2021), 2581-8147.
  • [26] H.M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(10), (2010), 1188-1192.
  • [27] H.M. Srivastava, S. Sivasubramanian and R. Sivakumar, Initial coefficients bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Mathematical Journal, 7(2), (2014), 1-10.
  • [28] H. M. Srivastava, A. Motamednezhad and E. A. Adegani, Faber polynomial coefficient estimates for bi-univalent functions defined by using differential subordination and a certain fractional derivative operator, Mathematics, 8 (2020), Article ID 172, 1-12.
  • [29] S. Sumer¨ Eker, Coefficients bounds for subclasses of m-fold symmetric bi-univalent functions, Turkish J. Math., 40(3), (2016), 641-646.
  • [30] A.k. Wanas, S. Yalc¸in, Horadam polynomials and their applications to new family of bi-univalent functions with respect to symmetric conjugate points, Proyecciones, 40, (2021), 107-116.
  • [31] A.k. Wanas, Applications of (M,N)-Lucas polynomials for holomorphic and bi-univalent functions, Filomat, 34, (2020), 3361-3368.
  • [32] H. M. Srivastava, A. K. Wanas, Initial Maclaurin coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination, Kyungpook Math. J., 59, (2019), 493-503.
  • [33] A. K. Wanas, A. L. Alina, Applications of Horadam polynomials on Bazilevicˇ bi-univalent function satisfying subordinate conditions, J. Phys. : Conf. Ser., 1294 (2019), 1-6.

Certain New Subclasses of $t$-fold Symmetric Bi-univalent Function Using $Q$-derivative Operator

Year 2021, Volume: 9 Issue: 1, 137 - 142, 28.04.2021

Timilehin Shaba

Abstract

In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with $q$-derivative operator; both $f(z)$ and $f^{-1}(z)$ are $t$-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients $|\rho_{t+1}|$ and $|\rho_{2t+1}|$ are found in this study. Also certain special cases are indicated. 

Keywords

t-fold symmetric bi-univalent functions analytic functions univalent function

References

  • [1] A. Akgul, Finding initial coefficients for a class of bi-univalent functions given by q-derivative, AIP Conference Proceedings ,1926, 020001(2018).
  • [2] A. Akgul, On the coefficient estimates of analytic and bi-univalent m-fold symmetric functions, Mathematica Aeterna, 7(3) (1993) 253-260.
  • [3] H. Aldweby and M. Darus, A subclass of harmonic U univalent functions associated with q-analogue of Dziok-Srivastava operator, ISRN Mathematical Analysis, 2013 (2013), Article ID 382312, 6 pages.
  • [4] H. Aldweby and M. Darus, Coefficient estimates for initial taylor-maclaurin coefficients for a subclass of analytic and bi-univalent functions associated with q-derivative operator, Recent Trends in Pure and Applied Mathematics, 2017 (2017).
  • [5] S¸. Altinkaya, S. Yalc¸in, On some subclasses of m-fold symmetric bi-univalent functions, Communications Faculty of Sciences University of Series A1: Mathematics and Statistics, 67(1) (2018) 29-36.
  • [6] A. Aral, V. Gupta and R. P. Agarwal, Application of q-Calculus in Operator Theory, Springer, New York, USA, 2013.
  • [7] D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Universitatis Babes¸-Bolyai, Mathematica, 31(2) (1986) 70-7.
  • [8] S. Bulut, Coefficient estimates for general subclasses of m-fold symmetric analytic bi-univalent functions, Turkish J. Math., 40, (2016) 1386-1397.
  • [9] S. Bulut, Certain subclasses of analytic and bi-univalent functions involving the q-derivative operator, Communications Faculty of Sciences University of Series A1: Mathematics and Statistics, 66(1) (2017) 108-114.
  • [10] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenchaften, Springer, New York, NY, USA, 1983.
  • [11] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (2004), 1529-1573.
  • [12] S.G Hamiidi and J.M. Jahangiri, Unpredictability of the coefficients of m-fold symmetric bi-starlike functions , Internat. J. Math., 25(7), (2014) 1-8.
  • [13] F. H. Jackson , On q-definite integrals, The Quarterly Journal of Pure and Applied Mathematics , 41 (1910), 193-203.
  • [14] F. H. Jackson , On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh , 46 (1908), 253-281.
  • [15] M. Lewin, On a coefficients problem of bi-univalent functions, Proc. Am. Math. Soc., 18 (1967), 63-68.
  • [16] A. Mohammmed, M. Darus, A generalized operator involving the q-hypergeometric function, Mat. Vesnik, 65 (2013), 454-465.
  • [17] F. Muge Sakar, M. O. Guney, Coefficient estimates for certain subclasses of m-mold symmetric bi-univalent functions defined by the q-derivative operator, Konuralp Journal of Mathematics, 6(2) (2018), 279-285.
  • [18] C.H. Pommerenke, Univalent Functions, Vandendoeck and Rupercht, Gottingen, 1975.
  • [19] T. M. Seoudy and M. K. Aouf, Convolution properties for C certain classes of analytic functions defined by q-derivative operator, Abstract and Applied Analysis, 2014 (2014), Article ID 846719, 7 pages.
  • [20] T. M. Seoudy and M. K. Aouf, Coefficient estimates of new classes of q-starlike and q-convex functions of complex order , Journal of Mathematical Inequalities , 10(1) (2016), 135-145.
  • [21] T. G. Shaba, On some new subclass of bi-univalent functions associated with the Opoola differential operator, Open J. Math. Anal., 4 (2), (2020), 74–79.
  • [22] T. G. Shaba, Certain new subclasses of m-fold symmetric bi-pseudo-starlike functions using Q-derivative operator, Open J. Math. Anal., 5 (1), (2021), 42–50.
  • [23] T. G. Shaba, Subclass of bi-univalent functions satisfying subordinate conditions defined by Frasin differential operator, Turkish Journal of Inequalities, 4 (2) (2020), 50–58.
  • [24] T. G. Shaba, On some subclasses of bi-pseudo-starlike functions defined by Salagean differential operator, Asia Pac. J. Math., 8 (6) (2021), 1–11; Available online at https://doi:10.28924/apjm/8-6 .
  • [25] T. G. Shaba, A. B. Patil, Coefficient estimates for certain subclasses of m-fold symmetric bi-univalent functions associated with pseudo-starlike functions, Earthline Journal of Mathematical Sciences, 6 (2) (2021), 2581-8147.
  • [26] H.M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(10), (2010), 1188-1192.
  • [27] H.M. Srivastava, S. Sivasubramanian and R. Sivakumar, Initial coefficients bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Mathematical Journal, 7(2), (2014), 1-10.
  • [28] H. M. Srivastava, A. Motamednezhad and E. A. Adegani, Faber polynomial coefficient estimates for bi-univalent functions defined by using differential subordination and a certain fractional derivative operator, Mathematics, 8 (2020), Article ID 172, 1-12.
  • [29] S. Sumer¨ Eker, Coefficients bounds for subclasses of m-fold symmetric bi-univalent functions, Turkish J. Math., 40(3), (2016), 641-646.
  • [30] A.k. Wanas, S. Yalc¸in, Horadam polynomials and their applications to new family of bi-univalent functions with respect to symmetric conjugate points, Proyecciones, 40, (2021), 107-116.
  • [31] A.k. Wanas, Applications of (M,N)-Lucas polynomials for holomorphic and bi-univalent functions, Filomat, 34, (2020), 3361-3368.
  • [32] H. M. Srivastava, A. K. Wanas, Initial Maclaurin coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination, Kyungpook Math. J., 59, (2019), 493-503.
  • [33] A. K. Wanas, A. L. Alina, Applications of Horadam polynomials on Bazilevicˇ bi-univalent function satisfying subordinate conditions, J. Phys. : Conf. Ser., 1294 (2019), 1-6.
There are 33 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Articles
Authors

Timilehin Shaba

Publication Date April 28, 2021
Submission Date September 11, 2020
Acceptance Date March 22, 2021
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

APA Shaba, T. (2021). Certain New Subclasses of $t$-fold Symmetric Bi-univalent Function Using $Q$-derivative Operator. Konuralp Journal of Mathematics, 9(1), 137-142.
AMA Shaba T. Certain New Subclasses of $t$-fold Symmetric Bi-univalent Function Using $Q$-derivative Operator. Konuralp J. Math. April 2021;9(1):137-142.
Chicago Shaba, Timilehin. “Certain New Subclasses of $t$-Fold Symmetric Bi-Univalent Function Using $Q$-Derivative Operator”. Konuralp Journal of Mathematics 9, no. 1 (April 2021): 137-42.
EndNote Shaba T (April 1, 2021) Certain New Subclasses of $t$-fold Symmetric Bi-univalent Function Using $Q$-derivative Operator. Konuralp Journal of Mathematics 9 1 137–142.
IEEE T. Shaba, “Certain New Subclasses of $t$-fold Symmetric Bi-univalent Function Using $Q$-derivative Operator”, Konuralp J. Math., vol. 9, no. 1, pp. 137–142, 2021.
ISNAD Shaba, Timilehin. “Certain New Subclasses of $t$-Fold Symmetric Bi-Univalent Function Using $Q$-Derivative Operator”. Konuralp Journal of Mathematics 9/1 (April 2021), 137-142.
JAMA Shaba T. Certain New Subclasses of $t$-fold Symmetric Bi-univalent Function Using $Q$-derivative Operator. Konuralp J. Math. 2021;9:137–142.
MLA Shaba, Timilehin. “Certain New Subclasses of $t$-Fold Symmetric Bi-Univalent Function Using $Q$-Derivative Operator”. Konuralp Journal of Mathematics, vol. 9, no. 1, 2021, pp. 137-42.
Vancouver Shaba T. Certain New Subclasses of $t$-fold Symmetric Bi-univalent Function Using $Q$-derivative Operator. Konuralp J. Math. 2021;9(1):137-42.
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