Coefficient bounds for a family of analytic functions linked with a petal-shaped domain and applications to Borel distribution. (English) Zbl 1538.30063
Summary: In this paper, by employing sine hyperbolic inverse functions, we introduced the generalized subfamily \(\mathcal{RK}_{\sinh}(\beta)\) of analytic functions defined on the open unit disk \(\Delta:=\{\xi: \xi \in \mathbb{C} \text{ and } |\xi|<1\}\) associated with the petal-shaped domain. The bounds of the first three Taylor-Maclaurin’s coefficients, Fekete-Szegö functional and the second Hankel determinants are investigated for \(f\in\mathcal{RK}_{\sinh}(\beta)\). We considered Borel distribution as an application to our main results. Consequently, a number of corollaries have been made based on our results, generalizing previous studies in this direction.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
Keywords:
analytic function; bounded turning function; convex function; subordination; Fekete-Szego functional; Hankel determinant; Borel distributionReferences:
| [1] | A. Alotaibi, M. Arif, M.A. Alghamdi and S. Hussain, Starlikeness associated with cosine hypergeometric function, Mathematics, 8 , Art. Id: 1118 (2020). |
| [2] | M. Arif, M. Raza, H. Tang, S. Hussain and H. Khan, Hankel de-terminant of order three for familiar subsets of analytic functions related with sine function, Open Math., 17 (2019), pp.1615-1630. · Zbl 1441.30019 |
| [3] | K. Bano and M. Raza, Starlike functions asscoiated with cosine function, Bull. Iran. Math. Soc., (2020). |
| [4] | D. Bansal, Upper bound of second Hankel determinant for a new class of analytic functions, Appl. Math. Lett., 26 (2013), pp.103-107. · Zbl 1250.30006 |
| [5] | O. Barukab, M. Arif, M. Abbas and S.K. Khan, Sharp bounds of the coefficient results for the family of bounded turning functions associated with petal-shaped domain, J. Funct. Spaces (2021), Art. Id: 5535629 (2021). · Zbl 1462.30025 |
| [6] | N.E. Cho, V. Kumar, S.S. Kumar and V. Ravichandran, Radius problems for starlike functions associated with sine functions, Bull. Iran. Math. Soc., 45 (2019), pp.213-232. · Zbl 1409.30009 |
| [7] | M. Fekete and G. Szegö, Eine Benberkungüber ungerada Schlichte funcktionen, J. London Math. Soc. , 8 (1933), pp.85-89. · JFM 59.0347.04 |
| [8] | M. H. Golmohammadi, S. Najafzadeh and M.R. Foroutan, Some Properties of Certain subclass of meromorphic functions associated with (p, q)-derivative, Sahand Commun. Math. Anal., 17 (4) (2020), pp. 71-84. · Zbl 1488.30072 |
| [9] | W. Janowski, Extremal problems for a family of functions with positive real part and for some related families, Ann. Polonic Math, 23 (1971), pp. 159-177. · Zbl 0199.39901 |
| [10] | A. Janteng, S.A. Halim and M. Darus,Coefficient inequality for a function whose derivative has a positive real part, J. Inequal. Pure Appl. Math., 7 (2)(2006), Art. 50, 5 pages. · Zbl 1134.30310 |
| [11] | A. Janteng, S.A. Halim and M. Darus, Hankel determinant for starlike and convex functions, Int. J. Math. Anal., 1 (13) (2007), pp. 619-625. · Zbl 1137.30308 |
| [12] | W. Koepf, On the Fekete-Szegö problem for close-to-convex func-tions , Proc. Amer. Math. Soc., 101 (1987), pp. 89-95. · Zbl 0635.30019 |
| [13] | S.S. Kumar and K. Arora, Starlike function associated with a petal shaped domain, arXiv Preprint 2010.10072. |
| [14] | S.K. Lee, V. Ravichandran and S. Subramaniam, Bounds for the second Hankel determinant of certain univalent functions, J. In-equal. Appl., 281 (2013), pp.1-17. · Zbl 1302.30018 |
| [15] | R.J. Libera and E.J. Zlotkiewicz, Coefficient bounds for the inverse of a function with derivative in P , Proc. Amer. Math. Soc., 87 (2) (1983), pp. 251-257. · Zbl 0488.30010 |
| [16] | R. Mendiratta, S. Nagpal and V. Ravichandran, On a subclass of strongly starlike functions associated with exponential fuction, Bull. Malays. Math. Sci. Soc., 38 (2015), pp. 365-386. · Zbl 1312.30019 |
| [17] | S.S. Miller and P.T. Mocanu, Differential Subordination: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, 225, CRC Press, 2000. · Zbl 0954.34003 |
| [18] | A.K. Mishra and T. Panigrahi, The Fekete-Szegö problem for a class defined by Hohlov operator, Acta Univ. Apul., 29 (2012), pp. 241-254. · Zbl 1289.30083 |
| [19] | R.N. Mohapatra and T. Panigrahi, Second Hankel determinant for a class of analytic functions defined by Komatu integral operator, Rend. Mat. Appl., 41 (1) (2020), pp. 51-58. · Zbl 1439.30030 |
| [20] | G. Murugusundaramoorthy and T. Bulboaca, Hankel determinants for new subclasses of analytic functions related to shell shaped re-gion, Mathematics, 8 (2020), 1041. |
| [21] | G. Murugusundaramoorthy and K. Vijaya, Certain subclasses of analytic functions associated with generalized telephone numbers, Symmetry, 2022, 14, 1053. |
| [22] | K.I. Noor and S.A. Shah, On certain generalized Bazilevic type functions associated with conic regions, Sahand Commun. Math. Anal., 17 (4) (2020), pp. 13-23. · Zbl 1474.30097 |
| [23] | C. Pommerenke, Univalent Functions, Studia Mathematica/ Math-ematische Lehrbucher, 25, Vandenhoeck and Ruprecht, Gottingen, Germany, (1975). · Zbl 0298.30014 |
| [24] | C. Pommerenke, On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc., 41 (1966), pp. 111-122. · Zbl 0138.29801 |
| [25] | C. Pommerenke, On the Hankel determinant of univalent function ,Mathematika, 14 (1967), pp. 108-112. · Zbl 0165.09602 |
| [26] | S.H. Sayedain Boroujeni and S.Najafzadeh, Error function and cer-tain subclasses of analytic univalent functions, Sahand Commun. Math. Anal., 20 (1) (2023), pp. 107-117. · Zbl 1524.30086 |
| [27] | K. Sharma, N.K. Jain and V. Ravichandran, Starlike functions associated with a cardioid, Afr. Mat., 27 (2016), pp. 923-939. · Zbl 1352.30015 |
| [28] | L. Shi, I. Ali, M. Arif, N.E. Cho, S. Hussain and H. Khan, A study of third Hankel determinant problem for certain subfamilies of anlaytic functions involving cardioid domain, Mathematics, 7 (2019), 418. |
| [29] | L. Shi, H.M. Srivastava, M. Arif, S.Hussain and H. Khan, An in-vestigation of the third Hankel determinant problem for certain sub-families of univalent functions involving the exponential function, Symmetry, 11 (2019), 598. · Zbl 1425.30021 |
| [30] | J. Sokòl and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike function, Zeszyty Naukowei oficyna Wydawnicza al. Powstańcòw Warszawy, 19 (1996), pp.101-105. · Zbl 0880.30014 |
| [31] | H.M. Srivastava, Operators of basic (or q-)calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Tran. Sci., 44 (2020), pp. 327-344. |
| [32] | A.K. Wanas and J.A. Khuttar, Applications of Borel distribution series on analytic functions, Earthline J. Math. Sci., 4 (1) (2020), pp. 71-82. |
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