90813218-4a55-44cb-b373-00544a4387dc20210216121905872wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS1109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40512720202720201910.37394/23206.2020.19http://wseas.org/wseas/cms.action?id=23185Third Hankel Determinant for A Class of Functions with Respect to Symmetric Points Associated with Exponential FunctionK.GaneshJMTK, Karimnagar, Telangana, INDIAR.Bharavi SharmaKakatiya University, Telangana, INDIAK.Rajya LaxmiTSWRDC, Warangal East, Telangana, INDIAThe purpose of the present work is to determine the possible upper bound of third order Hankel determinant for the functions starlike and convex with respect to symmetric points associated with exponential functions.472020472020133138https://www.wseas.org/multimedia/journals/mathematics/2020/a265106-1140.pdf10.37394/23206.2020.19.13http://www.wseas.org/multimedia/journals/mathematics/2020/a265106-1140.pdfR.M. Ali, S. K. Lee, V. Ravichandran, S. Supra-maniam, The Fekete-Szego coefficient functional for transforms of analytic functions.Bull.Iranian Math. Soc.Vol.35, No. 2, 2009,pp. 119-142.R.M. Ali, V. Ravichandran, N. Seenivasagan,Coefficient bounds for p-valent functions.Appl.Math. Comput.Vol.187, No. 1,2007, pp. 35-46.S. Altinkaya, S. Yalcin, Third Hankel determinant for Bazilevic functions,Advances in Math.,5(2016),Vol.5, No. 2, 2016, pp.91-96.K.O. Babalola, On Hankel determinant for some classes of univalent functions,Inequal. TheoryAppl., Vol.6, 2007, pp. 1-7.10.1016/j.aml.2012.04.002D. Bansal, Upper bound of second Hankel determinant for a new class of analytic functions.Appl. Math. Lett.Vol. 26, No. 1, 2013, pp.103-107.10.5556/j.tkjm.34.2003.269N.E. Cho, S. Owa, Shigeyoshi. On the Fekete-Szego problem for strongly α-quasi convex functions. Tamkang J. Math.Vol.34, No. 1,2003, pp. 21-28.N.E. Cho, S. Owa, On the Fekete-Szego problemfor stronglyα-logarithmic quasi convex functions.Southeast Asian Bull. Math.Vol. 28, No.3, 2004, pp. 421-430.10.7153/jmi-2017-11-36N.E. Cho, B. Kowalczyk, O.S. Kwon, A. Lecko,Y.J. Sim, Some coefficient inequalities related to the Hankel determinant for strongly star-like functions of order alpha.J. Math. Inequal.Vol.11, No. 2, 2017, pp. 429-439.10.1080/00029890.2000.12005236R. Ehrenborg, The Hankel determinant of exponential polynomials.Amer. Math.Monthly Vol.107 ,No. 6, 2000, pp. 557-560.10.1112/jlms/s1-8.2.85M. Fekete, G. Szego, Eine Bemerkung UberUngerade Schlichte Funktionen .J. London Math. Soc.Vol. 8, No. 2, 1933, pp.85-89.10.3390/sym10100501Hai-Yan Zhang, Huo Tang, Xiao-Meng Niu,Third Order Hankel determinant for certainclass of analytic functions related with exponential function, MDPI, SymmetryVol.10, 501,2018,doi:10.3390/sym.10100501.10.1088/1742-6596/1000/1/012056M. Haripriya,R.B. Sharma, On a class of bounded turning function subordinate to leaf like domain,J. Phy. Contemp Series 2018,1000-012056, doi:10.1088/1742-596 /1000/1/0102056.10.1112/plms/s3-18.1.77W.K. Hayman, On the second Hankel determinant of mean univalent functions.Proc. London Math. Soc.Vol. 3, No. 18, 1968, pp. 77-94.10.5556/j.tkjm.37.2006.148Janteng Aini, Halim Suzeini Abdul, Maslina Darus, Coefficient inequality for a function whose derivative has a positive real part. JIPAM.J. Inequal. Pure Appl. Math.Vol. 7, No. 2, 2006,Article 50, 5 pp.10.5556/j.tkjm.37.2006.148Janteng Aini, Halim Suzeini Abdul, Maslina Darus, Hankel determinant for star like and con-vex functions.Int. J. Math. Anal.(Ruse) 1(2007), no. 13-16, pp.619-625.10.1090/s0002-9939-1969-0232926-9F. R. Keogh, E. P. Merkes, A coefficient inequality for certain classes of analytic functions.Proc.Amer. Math. Soc.Vol. 20, 1969, pp. 8-12.10.1017/s0004972717001125B. Kowalczyk, A. Lecko, Y.J. Sim, The sharp bound for the Hankel determinant of the third kind for convex functions. Bull.Aust. Math. Soc.Vol .97, No. 3, 2018, pp.435-445.10.1155/2017/6476391K. Rajya Laxmi, R.Bharavi Sharma, SecondHankel determinants for some subclasses of biunivalent functions associated with pseudo-starlike functions.J. Complex Anal.2017, Art.ID 6476391, pp.1-9.10.1007/s11785-018-0819-0A. Lecko, Y.J. Sim, B. Smiarowska, The sharp bound of the Hankel determinant of the third kind for starlike functions of order 1/2, Complex Analysis and Operator Theory, Doi.org/10.1007/s11785-018-0819-0,July 2018.10.1186/1029-242x-2013-281S.K. Lee, V. Ravichandran, S. Supramaniam, Bounds for the second Hankel determinant of certain univalent functions.J. Inequal. Appl.,2013, 2013:281, 17 pp.Z. Lewandowski, S.S. Miller, E. Zlotkievicz, Gamma-Starlike functions. Ann. Univ. Math. J.,Vol. 27, No.4, 1978, pp.671-688.10.1090/s0002-9939-1983-0681830-8R. J. Libera, E. J. Zlotkiewicz, Coefficient bounds for the inverse of a function with derivative in .Proc. Amer. Math. Soc.Vol. 87, No. 2,1983, pp. 251-257.10.1155/2014/603180Liu Ming-Sheng, Xu Jun-Feng, Yang Ming, Up-per bound of second Hankel determinant for certain subclasses of analytic functions.Abstr. Appl.Anal.(2014), 2014, Art.ID 603180, pp.1-10.W.C. Ma, D. Minda, A unified treatment of some special classes of univalent functions. Proceedings of the Conference on Complex Analysis (Tianjin, 1992), 157-169, Conf. Proc. Lecture Notes Anal., I, Int. Press, Cambridge, MA, 1994, pp. 157-169.10.1007/s13370-018-0575-3N. Magesh, V. K. Balaji, Fekete-Szeg ̈oproblemfor a class of convex and starlike functions associated with kth root transformation using quasi-subordination.Afr. Mat.Vol.29, No. 5-6, 2018,pp. 775-782.10.1007/s40840-014-0026-8R. Mendiratta, S. Nagpal, V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function.Bull.Malays. Math.Sci. Soc.Vol. 38, No. 1, 2015, pp.365-386.10.22436/jmcs.018.04.06Mohd Narzan Mohammed Pauzi, M. Darus,Saibah Siregar, Second and third Hankel determinant for a class defined by generalized poly-logarithm functions, TJMM, Vol. 10 No. 1, 2018,pp.31-41.G. Murugusundaramurthy, S. Kavitha, T. Rosy,On the Fekete-Szego problems for Some Sub-classes of analytic functions defined by convolution, Proc. Pakistan ACAD Soc.,Vol.44,No.4,pp.249-254.10.1090/s0002-9947-1976-0422607-9J.W. Noonan, D.K. Thomas, On the second Hankel determinant of a really mean p-valent functions. Trans. Amer. Math. Soc.Vol. 223,1976, pp.337-346.K.I. Noor, Inayat. Hankel determinant problem for the class of functions with bounded boundary rotation.Rev. Roumaine Math. Pures Appl.Vol.28 , No. 8, 1983, pp.731-739.10.3906/mat-1505-3H. Orhan, N. Magesh, J. Yamini, Bounds for the second Hankel determinant of certain bi-univalent functions.Turkish J. Math.Vol. 40,No. 3, 2016, pp.679-687.10.1515/ausm-2015-0014J.K. Prajapat, D. Bansal, A. Singh, A. KMishra, Bounds on third Hankel determinant for close-to-convex functions. Acta Univ. Sapientiae Math.Vol.7, No. 2, 2015, pp.210-219.10.24193/subbmath.2017.2.05J.K. Prajapat, D. Bansal, S. Maharana, Boundson third Hankel determinant for certain classes of analytic functions.Stud. Univ. Babes-Bolyai Math., Vol.62, No. 2, 2017, pp.183-195.Ch. Pommerenke, Univalent functions,J. Math.Soc., Japan, Vol. 49,1975, pp.759-780.10.1112/jlms/s1-41.1.111Ch. Pommerenke, On the coefficients and Hankel determinants of univalent functions.J. Lon-don Math. Soc., Vol. 41, 1966, pp. 111-122.10.1112/s002557930000807xCh. Pommerenke, On the Hankel determinants of univalent functions. Mathematika Vol.14,1967, pp.108-112.10.1016/j.crma.2017.09.006D. Raducanu, P. Zaprawa Second Hankel determinant for close-to-convex functions. C. R.Math. Acad. Sci. Paris Vol. 355, No. 10, 2017,pp.1063-1071.R. K. Raina, J. Sok ́ol, On coefficient estimates for a certain class of starlike functions. Hacet. J.Math. Stat.Vol.44, No. 6, 2015, pp.1427-1433.T. Ram Reddy, R.B. Sharma, Fekete-Szeg ̈oin-equality for some subclasses of analytic functions involving complex order,Mathematical Sciences International Research Journal, Vol. 1,Issue-2, 2012.V. Ravichandran, Y. Polatoglu, M. Bolcal, A.Sen Certain subclasses of starlike and convex functions of complex order. Hacet. J. Math.Stat.Vol. 34 , 2005, pp.9-15.10.4134/bkms.2006.43.3.589T. N. Shanmugam, C. Ramachandran, V.Ravichandran, Fekete-Szego problem for sub-classes of starlike functions with respect to symmetric points.Bull. Korean Math. Soc.Vol. 43,No. 3, 2006, pp. 589-598.10.1007/s13226-013-0002-2T. Ram Reddy, R.B. Sharma, K. Saroja, A new subclass of meromorphic functions with positive coefficients. Indian J. Pure Appl. Math.Vol. 44,No. 1, 2013, pp. 29-46.10.1080/17476930108815351H. M. Srivastava, A. K. Mishra, M.K. Das, The Fekete-Szego problem for a subclass of close-to-convex functions. Complex Variables Theory Appl.Vol. 44 , No. 2, 2001, pp.145-163.N. Tuneski, M. Darus, Fekete-Szego functional for non-Bazilevic functions. Acta Math. Acad. Paedagog. Nyhzi. (N.S.) Vol.18, No. 2, 2002,pp.63-65.10.1080/17476933.2015.1012162D. Vamshee Krishna, B. Venkateswarlu, T. Ram-Reddy, Third Hankel determinant for certain subclass of p-valent functions.Complex Var. Elliptic Equ. Vol.60, No. 9, 2015, pp. 1301-1307.10.17951/a.2016.70.1.37D. Vamshee Krishna, B. Venkateswarlu, T. Ram-Reddy, Third Hankel determinant for starlikeand convex functions with respect to symmet-ric points.Ann. Univ. Mariae CurieSk ́łodowskaSect.Vol. 70, No. 1, 2016, pp.37-45.P. Zaprawa, On Hankel determinant H2(3) for univalent functions. Results Math., Vol. 73, No.3, 2018, Art. 89, pp.1-12.