Akgul, A. (2018). Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions. Sahand Communications in Mathematical Analysis, 11(1), 133-143. doi: 10.22130/scma.2018.61252.220

Arzu Akgul. "Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions". Sahand Communications in Mathematical Analysis, 11, 1, 2018, 133-143. doi: 10.22130/scma.2018.61252.220

Akgul, A. (2018). 'Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions', Sahand Communications in Mathematical Analysis, 11(1), pp. 133-143. doi: 10.22130/scma.2018.61252.220

Akgul, A. Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions. Sahand Communications in Mathematical Analysis, 2018; 11(1): 133-143. doi: 10.22130/scma.2018.61252.220

Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions

^{}Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli, Turkey.

Abstract

In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].

[1] A. Akgul and S. Altinkaya, Coefficient estimates associated with a new subclass of bi-univalent functions, Acta Univ. Apulensis Math. Inform., 52 (2017), pp. 121-128

[2] A. Akgul, Finding initial coefficients for a class of bi-univalent functions given by q-derivative, AIP Conference Proceedings, Vol. 1926. No. 1. AIP Publishing, 2018.

[3] A. Akgul, New subclasses of analytic and bi-univalent functions involving a new integral operator defined by polylogarithm function, Theory and Applications of Mathematics and Computer Science 7 (2017), pp. 31-40.

[4] A. Akgul, Coefficient estimates for certain subclass of bi-univalent functions obtained with polylogarithms,Mathematical Sciences And Applications E-Notes, 6 (2018), pp. 70-76.

[5] S. Altinkaya and S. Yalcin, Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math., 6 (2015), pp. 180-185.

[6] S. Altinkaya and S. Yalcin, Coefficient estimates for two new subclass of bi-univalent functions with respect to Symmetric Points, J. Funct. Spaces, 2015 (2015), 5 pages.

[7] S. Altinkaya and S. Yalcin, Coefficient problem for certain subclasses of bi-univalent functions defined by convolution, Math. Morav., 20 (2016), pp. 15-21.

[8] S. Bulut, Coefficient estimates for a new subclass of analytic and bi-univalent functions defined by Hadamard product, J. Complex Anal., 2014 (2014), 7 pages.

[9] D.A. Brannan and J.G. Clunie, Aspects of contemporary complex analysis, in Proceeding of the NATO Advanced Study Instutte Held at University of Durham: July, (1979), pp. 1-20, Academic Press, New York, N, YSA, 1980.

[10] M. Caglar, H. Orhan, and N. Yagmur, Coefficient bounds for new subclass of bi-univalent functions, Filomat, 27 (2013), pp. 1165-1171.

[11] O. Crisan, Coefficient estimates of certain subclass of bi-univalent functions, Gen. Math. Notes, 16 (2013), pp. 93-102.

[12] P.L. Duren, Grundlehren der Mathematischen Wissenchaften, Springer, New York, NY, USA,1983.

[13] B.A. Frasin and M.K. Aouf, New subclass of bi-univalent functions, Appl. Math. Lett., {24 (2011), pp. 1569-1573.

[14] M. Lewin, On a coefficient problem of bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), pp. 63-68.

[15] X.F. Li and A.P. Wang, Two new subclasses of bi-univalent functions, Int. Math. Forum, 7 (2012), pp. 1495-1504.

[16] N. Magesh and J. Yamini, Coefficient bounds for a certain subclass of bi-univalent functions, Int. Math. Forum 8 (22), (2013), pp. 1337-1344.

[17] E. Netanyahu, The minimal distance of the image boundary from the orijin and the second coefficient of a univalent function in $mid zmid <1$ , Arch. Ration. Mech. Anal., 32 (1969), pp. 100-112.

[18] C.H. Pommerenke, Univalent functions, Vandenhoeck and Rupercht, Gottingen, 1975.

[19] S. Ponnusamy, Inclusion theorems for convolution product of second order polylogariyhms and functions with the derivative in a half plane, Rocky Mountain J. Math., 28 (1998), pp. 695-733.

[20] S. Ponnusamy and S. Sabapathy, Polylogarithms in the theory of univalent functions, Results Math., 30 (1996), pp. 136-150.

[21] S. Porwal and M. Darus, On a new subclass of bi-univalent functions, J. Egypt. Math. Soc., 21 (2013), pp. 190-193

[22] St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc., 49 (1975), pp. 109-115.

[23] G.S. Salagean, Subclasses of univalent functions, Lecture Notes in Math., Springer Verlag, 1013 (1983), pp. 362-372.

[24] K. Al Shaqsi and M. Darus, An oparator defined by convolution involving the polylogarithms functions, Journal of Mathematics and Statics, 4 (2008), pp. 46-50.

[25] S. Siregar and M. Darus, New subclass of biunivalent functions involving the polylogarithms functions, Proceedings of the 3rd International Conference on Mathematical Sciences AIP Conf. Proc., 1602 (2014), pp. 893-898.

[26] H.M. Srivastava, A.K. Mishra, and P. Gochhayat, Certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), pp. 1188-1192.

[27] B. Srutha Keerthi and B. Raja, Coefficient inequality for certain new subclass of analytic bi-univalnt functions, Theoratical Mathematics and Applications, 3 (2013), pp. 1-10.

[28] Q.H. Xu, Y.C. Gui, and H.M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2012), pp. 990-994.

[29] Q.H. Xu, H.G. Xiao, and H.M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput.,218 (2012), pp. 11461-11465.

[30] Q.H. Xu, H.M. Srivastava, and Z. Li, A certain subclass of analytic and close-to-convex functions, Appl. Math. Lett., 24 (2011), pp. 396-401.