On H3(1) Hankel determinant for starlike and convex functions associated with exponential function
*Omar S. ErzigCorresponding authoroma22u2003@uoanbar.edu.iqDepartment of Mathematics College of Education for Pure Sciences University of Anbar Ramadi, Al-Anbar, IraqView full profile → , Abdul Rahman S. Jumaeps.abdulrahman.juma@uoanbar.edu.iqDepartment of Mathematics College of Education for Pure Sciences University of Anbar Department of Mathematics College of Education for Pure Sciences University of AnbarRamadi, Anbar, IraqView full profile → , Ali Al-Fayadhaalfayadh@yahoo.comDepartment of Mathematics and Computer Applications College of Science Al-Nahrain UniversityDepartment of Mathematics and Computer Applications College of Science Al–Nahrain UniversityBaghdad, 10072, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 12 Feb 2024
- Published Online:
- 30 Jun 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1909
- Pages:
- 897–905
Abstract
Keywords
Subject Classifications
References
[1] S. S. Miller and P. T. Mocanu, Differential subordinations: Theory and Application, Series on Monographs and Text-books in Pure and Applied Math., no. 225, Marcel Dekker Incorporated, New York and Basel, (2000).
[2] A. R. S. Juma, A. Al-Fayadh, S. P. Vijayalakshmi and T. V. Sudharsan, Upper bound on the third Hankel determinant for the class of univalent functions using an integral operator. Afr. Mat. 33 (2), 56, (2022).
[3] R. Mendiratta, S. Nagpal and V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function. Bull. Malays. Math. Sci. Soc. 38, 365–386, (2015). [CrossRef]
[4] A. R. S. Juma, M. H. Saloomi, Coefficient estimates for subclasses of regular functions. Iraqi Journal of Science, 59(3c), pp. 1710-1716, (2018).
[5] H-Y Zhang, H. Tang, X-M Niu. Third-Order Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function. Symmetry; 10(10):501, (2018).
[6] C. Pommerenke, G. Jensen, Univalent Functions; Vandenhoeck and Ruprecht: Gottingen, Germany, (1975).
[7] I. Efraimidis, A generalization of Livingston’s coefficient inequalities for functions with positive real part, J. Math. Anal. Appl. 435, 369-379, (2016).
[8] V. Ravichandran and S. Verma, Borne pour le cinquieme coefficient des function etoiles, Comptes Rendus Mathematique, (6)353, pp, 505-510, (2015).
[9] L. Shi, H. M. Srivastava, A. Rafiq, M. Arif and M. Ihsan, Results on Hankel determinants for the inverse of certain analytic functions subordinated to the exponential function, Mathematics, 10, 3429, (2022).
[10] F.R. Keogh and E.P. Merkes, A coefficient inequality for certain subclasses of analytic functions, Proc. Amer. Math. Soc. 20, 8-12, (1969). [CrossRef]
[11] M. Arif, M. Raza, H. Tang, S. Hussain and H. Khan, Hankel determinant of order three for familiar subsets of analytic functions related with sine function, Open Math. 17 (1), 1615-1630, (2019).
[12] C. Pommerenke, On the coefficients and Hankel determinants of univalent functions. J. Land. Math. Sec.1, 111-122, (1966). [CrossRef]
[13] C. Pommerenke, On the Hankel determinants of univalent functions. Mathematika. 14, 108-112, (1967). [CrossRef]
[14] A. Janteng, S. A. Halim and M. Darus, Coefficient inequality for a function whose derivative has a positive real part, J. Ineq. Pure Appl. Math. 7, 1–5, (2006).
[15] A. Janteng, S.A. Halim and M. Darus, Hankel determinant for starlike and convex functions. Int. J. Math. Anal. 1, 619–625, (2007).
[16] M. Fekete and G. Szegö, Eine benberkung uber ungerada schlichte funktionen. J. Lond. Math. Soc. 8, 85–89, (1933). [CrossRef]
[17] H. Tang, H. M. Srivastava, S. Sivasubramanian and P. Gurusamy, The Fekete-Szego functional problems for some classes of m-fold symmetric bi-univalent functions. J. Math. Inequal. 10, 1063–1092, (2016). [CrossRef].
[18] A. R. S. Juma and O. N. Kassar, Certain Properties for Analytic Functions Associated with q-Ruscheweyh Differential Operator. Iraqi Journal of Science, 61(9), 2350-2360, (2020).
[19] Abbood, Mohaimen M., Ebrahim, Hassan H., Al-Fayadh, Ali & Obaid, Ahmed J.(2023) Measure defined on Γ–algebra and some of their generalizations, Journal of Interdisciplinary Mathematics, 26:5, 821–827, DOI: 10.47974/JIM-1502.
