International Journal of Nonlinear Analysis and Applications
Coefficient estimates and Fekete-Szegő inequalities for a new subclass of m-fold symmetric bi-univalent functions satisfying subordinate conditions
Document Type : Research Paper
Authors
1 Department of Mathematics, Faculty of Mathematics and Computer Science, BabeÅŸ-Bolyai University, Cluj-Napoca, Romania
2 Department of Mathematics, Faculty of Arts and Science, Uludag University, Bursa, Turkey
Abstract
In this paper, we introduce a new subclass of the class of \textit{m}-fold symmetric bi-univalent functions and obtain estimates of the Taylor-Maclaurin coefficients $|a_{m+1}|,|a_{2m+1}|$ and Fekete-Szeg\H{o} functional problem for functions in this new subclass. The results in this paper generalize some of the results of Huo Tang et al. [18] Altinkaya and Yalcin [3].
Keywords
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[2] I. Aldawish, S.R. Swamy and B.A. Frasin, A special family of m-fold symmetric bi-univalent functions satisfying subordination condition, Fractal Fract. 6 (2022), no. 5, 271.
[3] S¸. Altınkaya and S. Yal¸cın, On a new subclass of bi-univalent functions satisfying subordinate conditions, Acta Univ. Sapientiae Math. 7 (2015), no. 1, 5–14.
[4] S¸. Altınkaya and S. Yal¸cın, On some subclasses of m-fold symmetric bi-univalent functions, Commun. Fac. Sci. Univ. Ank. S´er. A1 Math. Stat. 67 (2018), no. 1, 29–36.
[5] W.G. Atshan and S.K. Kazim, Coefficient estimates for some subclasses of bi-univalent functions related to m-fold symmetry, J. Al-Qadisiyah Comput. Sci. Math. 11 (2019), no. 2, 81–86.
[6] W.G. Atshan, S. Yal¸cın and R.A. Hadi, Coefficient estimates for special subclasses of k-fold symmetric bi-univalent functions, Math. Appl. 9 (2020), 83–90.
[7] S. Bulut, Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions, Commun. Fac. Sci. Univ. Ank. S´er. A1 Math. Stat. 68 (2019), no. 2, 1401–1410.
[8] G. Dong, T. Huo, A. En and X. Liang-Peng, Coefficient estimates for a class of m-fold symmetric bi-univalent function defined by subordination, Commun. Math. Res. 35 (2019), no. 1, 57–64.
[9] T.R.K. Kumar, S. Karthikeyan, S. Vijayakumar and G. Ganapathy, Initial coefficient estimates for certain subclasses of m fold symmetric bi-univalent functions, Adv. Dyn. Syst. Appl. 16 (2021), no. 2, 789–800.
[10] E. Mazi and S¸. Altınkaya, On a new sbclass of m-fold symmetric biunivalent functions equipped with subordinate conditions, Khayyam J. Math. 4 (2018), no. 2, 187–197.
[11] S.S. Miller and P.T. Mocanu, Differential Subordinations: Theory and Applications, Pure and Applied Mathematics No. 225, Marcel Dekker, New York, 2000.
[12] A. Motamednezhad and S. Salehian, Coefficient estimates for a general subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J. 12 (2019), no. 2, 163–176.
[13] A. Motamednezhad, S. Salehian and N. Magesh, The Fekete-Szego¨ problems for a subclass of m-fold symmetric bi-univalent functions, TWMS J. Appl. Eng. Math. 11 (2021), no. 2, 514–523.
[14] Ch. Pommerenke, On the coefficients of close-to-convex functions, Michigan Math. J. 9 (1962), 259–269.
[15] T.G. Shaba and A.B. Patil, Coefficient estimates for certain subclasses of m-fold symmetric bi-univalent functions associated with pseudo-starlike functions, Earthline J. Math. Sci.6 (2021), no. 2, 209–223.
[16] H.M. Srivastava and 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.
[17] S.R. Swamy, B.A. Frasin and I. Aldawish, Fekete-Szego¨ functional problem for a special family of m-fold symmetric bi-univalent functions, Mathematics 10 (2022), 1165.
[18] H. Tang, H.M. Srivastava, S. Sivasubramanian and P. Gurusamy, The Fekete-Szego¨ functional problems for some subclasses of m-fold symmetric bi-univalent functions, J. Math. Inequal. 10 (2016), 1063–1092.
[19] A.K. Wanas, Bounds for initial Maclaurin coefficients for a new subclasses of analytic and m-fold symmetric bi-univalent functions, TWMS J. Appl. Eng. Math. 10 (2020), no. 2, 305–311.
[20] A.K. Wanas and A.H. Majeed, Certain new subclasses of analytic and m-fold symmetric bi-univalent functions, Appl. Math. E-Notes 18 (2018), 178–188.
[21] A.K. Wanas and A.H. Majeed, On subclasses of analytic and m-fold symmetric bi-univalent functions, Iran. J. Math. Sci. Inf. 15 (2020), no. 2, 51–60.
[22] A.K. Wanas and A.O. P´all-Szab´o, ´ Coefficient bounds for new subclasses of analytic and m-fold symmetric biunivalent functions, Stud. Univ. Babe¸s-Bolyai Math. 66 (2021), no. 4, 659–666.
[2] I. Aldawish, S.R. Swamy and B.A. Frasin, A special family of m-fold symmetric bi-univalent functions satisfying subordination condition, Fractal Fract. 6 (2022), no. 5, 271.
[3] S¸. Altınkaya and S. Yal¸cın, On a new subclass of bi-univalent functions satisfying subordinate conditions, Acta Univ. Sapientiae Math. 7 (2015), no. 1, 5–14.
[4] S¸. Altınkaya and S. Yal¸cın, On some subclasses of m-fold symmetric bi-univalent functions, Commun. Fac. Sci. Univ. Ank. S´er. A1 Math. Stat. 67 (2018), no. 1, 29–36.
[5] W.G. Atshan and S.K. Kazim, Coefficient estimates for some subclasses of bi-univalent functions related to m-fold symmetry, J. Al-Qadisiyah Comput. Sci. Math. 11 (2019), no. 2, 81–86.
[6] W.G. Atshan, S. Yal¸cın and R.A. Hadi, Coefficient estimates for special subclasses of k-fold symmetric bi-univalent functions, Math. Appl. 9 (2020), 83–90.
[7] S. Bulut, Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions, Commun. Fac. Sci. Univ. Ank. S´er. A1 Math. Stat. 68 (2019), no. 2, 1401–1410.
[8] G. Dong, T. Huo, A. En and X. Liang-Peng, Coefficient estimates for a class of m-fold symmetric bi-univalent function defined by subordination, Commun. Math. Res. 35 (2019), no. 1, 57–64.
[9] T.R.K. Kumar, S. Karthikeyan, S. Vijayakumar and G. Ganapathy, Initial coefficient estimates for certain subclasses of m fold symmetric bi-univalent functions, Adv. Dyn. Syst. Appl. 16 (2021), no. 2, 789–800.
[10] E. Mazi and S¸. Altınkaya, On a new sbclass of m-fold symmetric biunivalent functions equipped with subordinate conditions, Khayyam J. Math. 4 (2018), no. 2, 187–197.
[11] S.S. Miller and P.T. Mocanu, Differential Subordinations: Theory and Applications, Pure and Applied Mathematics No. 225, Marcel Dekker, New York, 2000.
[12] A. Motamednezhad and S. Salehian, Coefficient estimates for a general subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J. 12 (2019), no. 2, 163–176.
[13] A. Motamednezhad, S. Salehian and N. Magesh, The Fekete-Szego¨ problems for a subclass of m-fold symmetric bi-univalent functions, TWMS J. Appl. Eng. Math. 11 (2021), no. 2, 514–523.
[14] Ch. Pommerenke, On the coefficients of close-to-convex functions, Michigan Math. J. 9 (1962), 259–269.
[15] T.G. Shaba and A.B. Patil, Coefficient estimates for certain subclasses of m-fold symmetric bi-univalent functions associated with pseudo-starlike functions, Earthline J. Math. Sci.6 (2021), no. 2, 209–223.
[16] H.M. Srivastava and 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.
[17] S.R. Swamy, B.A. Frasin and I. Aldawish, Fekete-Szego¨ functional problem for a special family of m-fold symmetric bi-univalent functions, Mathematics 10 (2022), 1165.
[18] H. Tang, H.M. Srivastava, S. Sivasubramanian and P. Gurusamy, The Fekete-Szego¨ functional problems for some subclasses of m-fold symmetric bi-univalent functions, J. Math. Inequal. 10 (2016), 1063–1092.
[19] A.K. Wanas, Bounds for initial Maclaurin coefficients for a new subclasses of analytic and m-fold symmetric bi-univalent functions, TWMS J. Appl. Eng. Math. 10 (2020), no. 2, 305–311.
[20] A.K. Wanas and A.H. Majeed, Certain new subclasses of analytic and m-fold symmetric bi-univalent functions, Appl. Math. E-Notes 18 (2018), 178–188.
[21] A.K. Wanas and A.H. Majeed, On subclasses of analytic and m-fold symmetric bi-univalent functions, Iran. J. Math. Sci. Inf. 15 (2020), no. 2, 51–60.
[22] A.K. Wanas and A.O. P´all-Szab´o, ´ Coefficient bounds for new subclasses of analytic and m-fold symmetric biunivalent functions, Stud. Univ. Babe¸s-Bolyai Math. 66 (2021), no. 4, 659–666.
[23] A.K. Wanas and H. Tang, Initial coefficient estimates for a classes of m-fold symmetric bi-univalent functions involving Mittag-Leffler function, Math. Morav. 24 (2020), no. 2, 51–61.
[24] A.K. Wanas and S. Yal¸cın, Initial coefficient estimates for a new subclasses of analytic and m-fold symmetric bi-univalent functions, Malaya J. Mate. 7 (2019), no. 3, 472–476.
[24] A.K. Wanas and S. Yal¸cın, Initial coefficient estimates for a new subclasses of analytic and m-fold symmetric bi-univalent functions, Malaya J. Mate. 7 (2019), no. 3, 472–476.
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Volume 14, Issue 1
January 2023Pages 3145-3154
- Receive Date: 27 October 2022
- Accept Date: 24 November 2022