Certain Subclass of Analytic Functions Defined by Wanas Operator

  • Timilehin Gideon Shaba Department of Mathematics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria
  • Abbas Kareem Wanas Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, Iraq
  • Ismaila Omeiza Ibrahim Department of Mathematical science, University of Maiduguri, Nigeria
Keywords: analytic function, starlike function, convex function, Wanas operator, subordination


In present article, we introduce and study a certain family of analytic functions defined by Wanas operator in the open unit disk. We establish some important geometric properties for this family. Further we point out certain special cases for our results.


J. W. Alexander, Functions which map the interior of the unit circle upon simple region, Ann. of Math. (2) 17 (1915), 12-22. https://doi.org/10.2307/2007212

F. M. Al-Oboudi, On univalent functions defined by a generalized Sălăgean operator, Int. J. Math. Math. Sci. 27 (2004), 1429-1436. https://doi.org/10.1155/S0161171204108090

S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446. https://doi.org/10.1090/S0002-9947-1969-0232920-2

K. O. Babalola, Combinations of geometric expressions implying schlichtness, An. Univ. Oradea Fasc. Mat. 21 (2014), 91-94.

A. Cătaş and A. A. Lupas, On a subclass of analytic functions defined by a generalized {S}u{a}lu{a}gean operator, ROMAI J. 4(2) (2008), 57-60.

N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling 37 (2003), 39-49. https://doi.org/10.1016/S0895-7177(03)80004-3

B. A. Frasin and M. Darus, On certain analytic univalent functions, Int. J. Math. Math. Sci. 25 (2001), 305-310. https://doi.org/10.1155/S0161171201004781

B. A. Frasin and J.M. Jahangiri, A new and comprehensive class of analytic functions, An. Univ. Oradea Fasc. Mat. 15 (2008), 59-62.

I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl. 176 (1993), 138-147. https://doi.org/10.1006/jmaa.1993.1204

G. Şt. Sălăgean, Subclasses of univalent functions, Lecture Notes in Math., Springer Verlag, Berlin 1013 (1983), 362-372. https://doi.org/10.1007/BFb0066543

T. G. Shaba, A. A. Ibrahim, L. O. Ahmed, On a comprehensive class of p-valent functions defined by generalized Al-Oboudi differential operator, Advances in Mathematics: Scientific Journal 9(12) (2020), 10633-10638. https://doi.org/10.37418/amsj.9.12.48

T. G. Shaba, On certain analytic functions defined by Frasin differential operator, Int. J. Open Problems Complex Analysis 12(3) (2020), 13-18.

H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination, Integral Transforms Spec. Funct. 18 (2007), 207-216. https://doi.org/10.1080/10652460701208577

S. R. Swamy, Inclusion properties of certain subclasses of analytic functions, Int. Math. Forum 7 (2012), 1751-1760.

B. A. Uralegaddi and C. Somanatha, Certain classes of univalent functions, in: Current Topics in Analytic Function Theory, Edited by H. M. Srivastava and S. Own, 371–374, World Scientific, Singapore, 1992. https://doi.org/10.1142/9789814355896_0032

A. K. Wanas, New differential operator for holomorphic functions, Earthline J. Math. Sci. 2 (2019), 527-537. https://doi.org/10.34198/ejms.2219.527537

A. K. Wanas and G. Murugusundaramoorthy, Differential sandwich results for Wanas operator of analytic functions, Math. Morav. 24 (2020), 17-28. https://doi.org/10.5937/MatMor2001017K

How to Cite
Shaba, T. G., Wanas, A. K., & Ibrahim, I. O. (2021). Certain Subclass of Analytic Functions Defined by Wanas Operator. Earthline Journal of Mathematical Sciences, 7(1), 137-144. https://doi.org/10.34198/ejms.7121.137144

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