# The Fekete-Szeg{\"o} inequality for certain class of analytic functions defined by convolution between generalized Al-Oboudi differential operator and Srivastava-Attiya integral operator

## Main Article Content

## Abstract

The aim of this paper is to investigate the Fekete Szeg{\"o} inequality for subclass of analytic functions defined by convolution between generalized Al-Oboudi differential operator and Srivastava-Attiya integral operator. Further, application to fractional derivatives are also given.

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## References

[1] M. Abramowitz, I.A. Stegun, Handbook of mathematical functions, Applied Mathematics Series, 55(62),p.39, 1966. Google Scholar

[2] F.M. Al-Oboudi, On univalent functions defined by a generalized S˘aL˘agean operator, International Journal of Mathematics and Mathematical Sciences, 2004(27), 1429–1436, 2004. Google Scholar

[3] K. Al Shaqsi and M. Darus, On coefficient problems of certain analytic functions involving Hadamard products, International Mathematical Forum, 1, 1669–1676, 2006. Google Scholar

[4] K.Al-Shaqsi and M. Darus, On univalent functions with respect to k-symmetric points defined by a generalized Ruscheweyh derivatives operator, Journal of Analysis and Applications, 7(1), 53–61, 2009. Google Scholar

[5] K. R. Alhindi, M. Darus, Fekete-Szeg¨o inequalities for Sakaguchi type functions and fractional derivative operator, AIP Conference Proceedings, 1571, 956–962, 2013. Google Scholar

[6] M.K. Aouf and F.M. Abdulkarem, Fekete–Szeg¨o inequalities for certain class of analytic functions of complex order, International Journal of Open Problems in Complex Analysis, 6(1),1-13, 2014 Google Scholar

[7] M.K. Aouf, R.M. El-Ashwah, A.A.M. Hassan and A.H. Hassan, Fekete–Szeg¨o problem for a new class of analytic functions defined by using a generalized differential operator, Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium. Mathematica, 52(1), 21–34, 2013. Google Scholar

[8] M. Arif, M. Darus, M. Raza, and Q. Khan, Coefficient bounds for some families of starlike and convex functions of reciprocal order, The Scientific World Journal, 2014, 1-6, 2014. Google Scholar

[9] K. A. Challab, M. Darus, and F. Ghanim, Certain problems related to generalized Srivastava–Attiya operator, Asian-European Journal of Mathematics, 10(2), 21 pages, 2017. Google Scholar

[10] M. Darus, and R.W. Ibrahim, On subclasses for generalized operators of complex order, Far East Journal of Mathematical Sciences, 33(3), 299–308, 2009. Google Scholar

[11] M. Fekete and G.Szeg¨o, Eine Bemerkung uber ungerade schlichte funktionen, J. London Math. Soc., 8(1933), 85-89. Google Scholar

[12] B. Frasin , Coefficient inequalities for certain classes of Sakaguchi type functions, Int. J. Nonlinear Sci, 10(2), 206–211, 2010. Google Scholar

[13] R. M. Goat, B. S. Marmot, On the coefficients of a subclass of starlike functions, Indian J. Pure Appl. Math, 12(5), 634–647, (1981) . Google Scholar

[14] F.R. Keogh and E.P. Merkes, A coefficient inequality for certain classes of analytic function, Proc. Amer. Math. Soc., 20(1969),8-12. Google Scholar

[15] W. Koeph, On the Fekete-Szeg¨o problem for close-to-convex functions, Proc. Amer. Math. Soc., 101(1987),89-95. Google Scholar

[16] T. Mathur and R. Mathur, Fekete-Szeg¨o inequalities for generalized Sakaguchi type functions, In Proceedings of the World Congress on Engineering, 1, 210-213, 2012. Google Scholar

[17] H. Orhan and E. Gunes, Fekete-Szeg¨o inequality for certain subclass of analytic functions, General Math, 14(1), 41–54, 2005. Google Scholar

[18] S. Owa and H.M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canadian Journal of Mathematics, 5, 1057–1077, 1987. Google Scholar

[19] S.F. Ramadan and M. Darus, On the Fekete-Szeg¨o inequality for a class of analytic functions defined by using generalized differential operator, Acta Universitatis Apulensis, 26, 167–78, 2011. Google Scholar

[20] V. Ravichandran, A. Gangadharan and M. Darus, Fekete-Szeg¨o inequality for certain class of Bazilevic functions, Far East Journal of Mathematical Sciences, 15(2), 171–180, 2004. Google Scholar

[21] T.R. Reddy and R.B. Sharma, Fekete–Szeg¨o inequality for some sub-classes of analytic functions defined by a differential operator, Indian Journal of Mathematics and Mathematical Sciences, 8(1), 115–126, 2012. Google Scholar

[22] Salagean and G. Stefan, Subclasses of univalent functions, Complex Analysis Fifth Romanian-Finnish Seminar, 362–372,1983. Google Scholar

[23] C. Selvaraj and T.R.K. Kumar, Fekete-Szeg¨o problem for some subclasses of complex order related to Salagean operator, Asian Journal of Mathematics and Applications, 2014, 1-9, 2014. Google Scholar

[24] T.N. Shanmugam, S. Kavitha and S. Sivasubramanian, On the Fekete-Szeg¨o problem for certain subclasses of analytic functions, Vietnam Journal of Mathematics, 36, 39–46, 2008. Google Scholar

[25] P. Sharma, R. K. Raina, and J. Sok´o l, On the convolution of a finite number of analytic functions involving a generalized Srivastava–Attiya operator, Mediterranean Journal of Mathematics, 13(4), 1535-1553, 2016. Google Scholar

[26] G. Singh and G. Singh, Second Hankel determinant for subclasses of starlike and convex functions, Open Science Journal of Mathematics and Application, 2(6), 48-51, 2015. Google Scholar

[27] H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination, Integral Transforms and Special Functions, 18(3), 2007, 207–216. Google Scholar

[28] H.M. Srivastava and A.K. Mishra, Applications of fractional calculus to parabolic starlike and uniformly convex functions, Computers and Mathematics with Applications, 39(3), 57–69, 2000. Google Scholar