Korean J. Math.  Vol 26, No 2 (2018)  pp.191-214
DOI: https://doi.org/10.11568/kjm.2018.26.2.191

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

Khalid Challab, Maslina Darus, Firas Ghanim


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.


Analytic functions; Starlike functions; Convex functions; Subordination; Schwarz Function; Fekete-Szego inequality; Generalized Al-Oboudi differential operator; Srivastava-Attiya integral operator.

Subject classification

30C45; 30C50


The work here is supported by UKM’s grant:GUP-2017-064.

Full Text:



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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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

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)

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)

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

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)

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

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

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)

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)

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)

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

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)

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)

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)

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)

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)

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)


  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr