1. bookVolume 30 (2022): Edition 1 (February 2022)
Détails du magazine
License
Format
Magazine
eISSN
1844-0835
Première parution
17 May 2013
Périodicité
1 fois par an
Langues
Anglais
access type Accès libre

On the Upper Bound of the Third Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function

Publié en ligne: 12 Mar 2022
Volume & Edition: Volume 30 (2022) - Edition 1 (February 2022)
Pages: 75 - 89
Reçu: 30 Dec 2020
Accepté: 28 May 2021
Détails du magazine
License
Format
Magazine
eISSN
1844-0835
Première parution
17 May 2013
Périodicité
1 fois par an
Langues
Anglais
Abstract

In the present paper we introduce a new class of analytic functions f in the open unit disk normalized by f(0) = f(0)1 = 0, associated with exponential functions. The aim of the present paper is to investigate the third-order Hankel determinant H3(1) for this function class and obtain the upper bound of the determinant H3(1).

Keywords

MSC 2010

[1] Bieberbach, L.:Über die Koeffizienten derjenigen Potenzreihein welche eine schlichte Abbildung des Einheitskreises veritteln, Reimer in Komm: Berlin, Germany, (1916). Search in Google Scholar

[2] De Branges, L.: A proof of the Bieberbach conjecture. Acta Math. 154 (1), 137–152 (1985).10.1007/BF02392821 Search in Google Scholar

[3] Cho, N.E., Kumar, V., Kumar, S.S., Ravichandran, V.: Radius problems for starlike functions associated with the sine function. Bull. Iran. Math. Soc. 45, 213–232 (2019). Search in Google Scholar

[4] Dienes, P.: The Taylor Series: An Introduction to the Theory of Functions of a Complex Variable. NewYork-Dover: Mineola, NY, USA, (1957). Search in Google Scholar

[5] Duren, P. L.: Univalent Functions. vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, (1983). Search in Google Scholar

[6] Ehrenborg, R.: The Hankel determinant of exponential polynomials. Amer. Math. Monthly, 107, 557–560 (2000).10.1080/00029890.2000.12005236 Search in Google Scholar

[7] Fekete, M., Szegö, G.: Eine Benberkung uber ungerada Schlichte funktionen. J. London Math. Soc. 8, 85–89 (1933). Search in Google Scholar

[8] Janowski, W.: Extremal problems for a family of functions with positive real part and for some related families. Annales Polonici Mathematici. 23, 159-177 (1970).10.4064/ap-23-2-159-177 Search in Google Scholar

[9] Keogh, F.R., Merkes, E.P.: A coefficient inequality for certain classes of analytic functions. Proc. Am. Math. Soc. 20, 8-12 (1969). Search in Google Scholar

[10] Libera R. J., Złotkiewicz E. J.: Early coefficients of the inverse of a regular convex function. Proc. Amer. Math. Soc. 85(2), 225-230 (1982). Search in Google Scholar

[11] Libera R. J., Złotkiewicz E. J.: Coefficient bounds for the inverse of a function with derivative in 𝒫. Proc. Amer. Math. Soc. 87(2), 251-257 (1983). Search in Google Scholar

[12] Ma, W., Minda. D.: A unified treatment of some special classes of univalent functions. Proceedings of the International Conference on Complex Analysis at the Nankai Institute of Mathematics, Tianjin, pp. 157-169 (1992). Search in Google Scholar

[13] Mendiratta, R., Nagpal, S., Ravichandran, V.: On a subclass of strongly starlike functions associated with exponential function. Bull. Malays. Math. Sci. Soc. 38, 365–386 (2015). Search in Google Scholar

[14] Miller, S.S., Mocanu, P.T.: Differential Subordination. Theory and Applications. Pure and Applied Mathematics, Marcel Dekker Inc., p. 225 (2000).10.1201/9781482289817 Search in Google Scholar

[15] Noonan, J. W., Thomas, D. K.: On the second Hankel determinant of areally mean p-valent functions. Trans. Amer. Math. Soc. 223(2), 337–346 (1976). Search in Google Scholar

[16] Noor, K. I.: On analytic functions related with function of bounded boundary rotation. Comment. Math. Univ. St. Pauli. 30(2), 113–118 (1981). Search in Google Scholar

[17] Noor, K. I.: Hankel determinant problem for the class of function with bounded boundary rotation. Rev. Roum. Math. Pures Et Appl. 28, 731–739 (1983). Search in Google Scholar

[18] Noor, K. I., Al-Bany, S. A.: On Bazilevic functions. Int. J. Math. Math. Sci. 10(1), 79–88 (1987). Search in Google Scholar

[19] Noor, K. I.: Higer order close-to-convex functions. Math. Japon. 37(1), 1–8 (1992). Search in Google Scholar

[20] Padmanabhan, K.S., Parvatham, R.: Some applications of differential subordination. Bull. Aust. Math. Soc. 32, 321-330 (1985). Search in Google Scholar

[21] Pommerenke, C., Jensen, G.: Univalent Functions. Vandenhoeck and Ruprecht: Gottingen, Germany, (1975). Search in Google Scholar

[22] Pommerenke, C.: On the coefficients and Hankel determinant of univalent functions. J. Lond. Math. Soc. 41, 111-112 (1966). Search in Google Scholar

[23] Shanmugam, T.N.: Convolution and differential subordination. Int. J. Math. Math. Sci. 12, 333-340 (1989). Search in Google Scholar

[24] Sókol, J., Stankiewicz, J.: Radius of convexity of some subclasses of strongly starlike functions. Zeszyty Naukowe/Oficyna Wydawnicza al. Powstanców Warszawy. 19, 101–105 (1996). Search in Google Scholar

[25] Srivastava, H.M., Owa, S. (Eds.): Current Topics in Analytic Function Theory, World Scientific Publishing Company, London, UK. (1992).10.1142/1628 Search in Google Scholar

Articles recommandés par Trend MD

Planifiez votre conférence à distance avec Sciendo