1. bookVolume 78 (2021): Issue 1 (October 2021)
Journal Details
License
Format
Journal
eISSN
1338-9750
First Published
12 Nov 2012
Publication timeframe
3 times per year
Languages
English
access type Open Access

A Certain Subclass of Analytic Functions with Negative Coefficients Defined by Gegenbauer Polynomials

Published Online: 01 Jan 2022
Volume & Issue: Volume 78 (2021) - Issue 1 (October 2021)
Page range: 73 - 84
Received: 11 Nov 2020
Journal Details
License
Format
Journal
eISSN
1338-9750
First Published
12 Nov 2012
Publication timeframe
3 times per year
Languages
English
Abstract

In this paper, we introduce a new subclass of analytic functions with negative coefficients defined by Gegenbauer polynomials. We obtain coefficient bounds, growth and distortion properties, extreme points and radii of starlikeness, convexity and close-to-convexity for functions belonging to the class TSλm(γ,e,k,v)TS_\lambda ^m(\gamma ,e,k,v). Furthermore, we obtained the Fekete-Szego problem for this class.

Keywords

[1] COHL, H.S.: On a generalization of the generating function for Gegenbauer polynomials, Int. Transf. Spec. Funct. 24 (2013), no. 10, 807–816. Search in Google Scholar

[2] DUREN, P. L.: Univalent Functions, A series of Comprehensive Studies in Mathematics, Vol. 259. Springer-Verlag, Berlin, 1983. Search in Google Scholar

[3] GOODMAN, A. W.: On uniformly convex functions, Ann. Polon. Math. 56 (1991), no. 1, 87–92. Search in Google Scholar

[4] GOODMAN, A. W.: On uniformly starlike functions, J. Math. Anal. Appl. 155 (1991), no. 2, 364–370. Search in Google Scholar

[5] KANAS, S.—SRIVASTAVA, H. M.: Linear operators associated with k-uniformly convex functions, Int. Transf. Spec. Funct. 9(2000), no. 2, 121–132. Search in Google Scholar

[6] KIEPIELA, K.—NARANIECKA, I.—SZYNAL, J.: The Gegenbauer polynomials and typically real functions, J. of Comput. and Appl. Math. 153 (2003), 273–282.10.1016/S0377-0427(02)00642-8 Search in Google Scholar

[7] MA, W.—MINDA, D.: Uniformly convex functions, Ann. Polon. Math. 57 (1992), 165–175.10.4064/ap-57-2-165-175 Search in Google Scholar

[8] MA, W. C.—MINDA, D.: A unified treatment of some special classes of univalent functions, In: Proceedings of the Conference on Complex Analysis, (Tianjin, 1992, Peoples Republic of China); June (1992) pp. 19–23; (Z. Li, F. Ren, L. Yang and S. Zhang, eds.), Conf. Proc. Lecture Notes Anal. I, Int. Press, Cambridge, MA, 1994, pp. 157–169. Search in Google Scholar

[9] OLATUNJI, S. O.—GBOLAGADE, A. M.: On certain subclass of analytic functions associated with Gegenbauer polynomials, J. Fract. Calc. Appl. 9 (2018), no. 2, 127–132. Search in Google Scholar

[10] POMMERENKE, C.: Univalent Functions. Vandenhoeck and Ruprecht, Gottingen, 1975. Search in Google Scholar

[11] RONNING, F.: Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993), no 1, 189–196. Search in Google Scholar

[12] SCHOBER, G.: Univalent Functions-Selected topics. In: Lecture Notes in Math. Vol. 478, Springer-Verlag, Berlin, 1975.10.1007/BFb0077279 Search in Google Scholar

[13] SILVERMAN, H.: Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109–116.10.1090/S0002-9939-1975-0369678-0 Search in Google Scholar

[14] SOBCZAK-KNEĆ, M.—ZAPRAWA, P.: Covering domains for classes of functions with real coefficients, Complex Var. Elliptic Equ. 52 (2007), no. 6, 519–535. Search in Google Scholar

[15] SWAPNA, G.—VENKATESWARLU, B.—REDDY, P. THIRUPATHI: Subclass of analytic functions defined by generalized differential operator, Acta Univ. Apulensis, Math. Inform. 62 (2020), 57–70. Search in Google Scholar

[16] SZYNAL, J.: An extension of typically real functions, Ann. Univ. Mariae Curie-Sklodowska, Sect. A. 48 (1994), 193–201. Search in Google Scholar

[17] ZAPRAWA, P.—FIGIEL, M.—FUTA, A.: On coefficients problems for typically real functions related to Gegenbauer polynomials, Mediterr. J. Math. 14 (2017), no. 2, Paper no. 99. Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo