Extensions of coefficient estimates for new classes of bi-univalent functions defined by Sălăgean integro-differential operator

• Autorzy: Páll-Szabó Ágnes Orsolya

Identyfikatory

DOI

10.1515/jaa-2020-2035

• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce and investigate three new general classes of bi-starlike and bi-convex functions of Ma-Minda type defined by the Sălăgean integro-differential operator. Bounds of the first three coefficients |a₂|, |a₃| and |a₄| are given.

Słowa kluczowe

EN

bi-univalent functions; bi-convex functions; bi-starlike functions; analytic functions; Salagean integral operator; Sălăgean differential operator; coefficient bounds

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2021
• Tom: Vol. 27, nr 1
• Strony: 87--95
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Páll-Szabó Ágnes Orsolya

• Department of Statistics-Forecasts-Mathematics, Faculty of Economics and Business Administration, Babeş-Bolyai University, Cluj-Napoca, Romania

• https://orcid.org/0000-0003-3469-3362

Bibliografia

• [1] J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. of Math. (2) 17 (1915), no. 1, 12-22.
• [2] 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 (2012), no. 3, 344-351.
• [3] C. Altınkaya and S. Yalçın, Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Math. Acad. Sci. Paris 353 (2015), no. 12, 1075-1080.
• [4] D. A. Brannan, J. Clunie and W. E. Kirwan, Coefficient estimates for a class of star-like functions, Canadian J. Math. 22 (1970), 476-485.
• [5] M. Çağlar and E. Deniz, Initial coefficients for a subclass of bi-univalent functions defined by Salagean differentia operator, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 66 (2017), no. 1, 85-91.
• [6] P. L. Duren, Univalent Functions, Grundlehren Math. Wiss. 259, Springer, New York, 1983.
• [7] B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), no. 9, 1569-1573.
• [8] J. M. Jahangiri and S. G. Hamidi, Faber polynomial coefficient estimates for analytic bi-Bazilevič functions, Mat. Vesnik 67 (2015), no. 2, 123-129.
• [9] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63-68.
• [10] W. C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis (Tianjin 1992), Conf. Proc. Lecture Notes Anal. 1, International Press, Cambridge (1994), 157-169.
• [11] S. S. Miller and P. T. Mocanu, Differential Subordinations, Monogr. Textb. Pure Appl. Math. 225, Marcel Dekker, New York, 2000.
• [12] A. O. Páll-Szabó, On a class of univalent functions defined by Sˇalˇagean integro-differential operator, Miskolc Math. Notes 19 (2018), no. 2, 1095-1106.
• [13] C. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975.
• [14] G. C. Sălăgean, Subclasses of univalent functions, in: Complex Analysis—Fifth Romanian-Finnish Seminar. Part 1 (Bucharest 1981), Lecture Notes in Math. 1013, Springer, Berlin (1983), 362-372.
• [15] D. L. Tan, Coefficient estimates for bi-univalent functions, Chinese Ann. Math. Ser. A 5 (1984), no. 5, 559-568.
• [16] L. Xiong and X. Liu, Some extensions of coefficient problems for bi-univalent Ma-Minda starlike and convex functions, Filomat 29 (2015), no. 7, 1645-1650.
• [17] Q.-H. Xu, Y.-C. Gui and H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), no. 6, 990-994.
• [18] Q.-H. Xu, H.-G. Xiao and H. M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218 (2012), no. 23, 11461-11465.
• [19] A. Zireh and S. Hajiparvaneh, Coefficient bounds for certain subclasses of analytic and bi-univalent functions, Ann. Acad. Rom. Sci. Ser. Math. Appl. 8 (2016), no. 2, 133-144.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)