On unified subclass of univalent functions of complex order using the Frasin operator

Vidyadhar Sharma; Nisha Mathur

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P524

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P524 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P524

On unified subclass of univalent functions of complex order using the Frasin operator

Vidyadhar Sharma, Nisha Mathur

Abstract

In the present investigation, we consider a unified class of univalent functions of complex order defined in the open unit disk U involving the Frusin operator. Some known consequences of the results are also derived.

Keywords

Analytic functions, Univalent functions, Starlike functions, Complex order and Subordination.

References

[1] M.S. Robertson, On the theory of univalent functions, Ann. Math. 37 (1936) 376-408
[2] P. Wiatrowski, On the coefficient of some family of holomorphic functions, ZeszytyNauk. Uniw.OdzNauk. Mat. –Przyrod. 39 (1970) 75-85.
[3] M.A. Nasr, M.K. Aouf, On convex functions of complex order, Mansoura Bull. Sci. 8 (1982) 565-582.
[4] S.Ruscheweyh, Convolutions in Geometric Function Theory, Presses Univ. Montreal, Montreal, Quebec, 1982.
[5] G.S. Salagean, Subclasses of univalent functions, Lecturer Notes in Mathematics, vol. 12. Springer- verlag, 1983, pp. 362-372.
[6] M.A. Nasr, M.K. Aouf, Starlike functions of complex order, J. Nat. Sci. Math. 23 (1985) 1-12.
[7] M. Obradovic, M.K. Aouf, S. Owa, On some results for starlike functions of complex, Publ. Inst. Math, .Nour. Ser. 46 (60) (1989) 79-85.
[8] W.C. Ma, D. Minda, A unified treatment of some special classes of univalent functions, in: Proceeding of the conference on complex analysis (Tianjin, 1992), Internat. Press, Cambridge, MA, pp. 157-169.
[9] S.S Miller, P.T. Mocanu, Differential subordination: theory and applications, Series on Monographs and Textbooks in pure and applied Mathematics, vol. 225, Marcel Dekker, New York, Basel, 2000.
[10] F.M. Al-Oboudi, M.M. Haidan, Spirallike functions of complex oeder, J. Not. Geom.19 (2000), 53-72.
[11] F.M. Al-Oboudi, on univalent functions defined by a generalized, Salagean operator, int. J. Math. Sci. (2004). No.25-28, 1429-1436.
[12] M.K. Aouf, F.M. Al-Oboudi, M.M. Haidan, On some results for λ - Spirallike and λ Robertson functions of complex order, Publ. Instit. Math. Belgrade 77 (91) (2005) 93-98.
[13] V. Ravichandran, Y. Polatoglu, M. Bolcal, A. Sen, Certain subclasses of starlike and convex functions of complex order, Hacettepe J. Math. Stat. 34 (2005) 9-15.
[14] H.M Srivastava, A .Y. Lashin, some application of the Briot-Bouquet differential subordination, J. Inequal. Pure. Appl. Math. 6(2) (2005) 1-7 (Art. 41).
[15] B.A. Frasin, Family of analytic functions of complex order, Acta. Math. Acad. Paedagog. Nyhazi. (NS) 22 (2) (2006) 179-191.
[16] T.N. Shanmugam, S. Sivasubramanian, S. Kavitha, On certain subclasses of functions of complex order, South. Asian Bull. Math.33 (2009) 535-541.
[17] T.M. Seoudy, On unified subclass of univalent functions of complex order involving the Salagean operator, J. Egyptain Math. Soc. (2013) 21, 194-196.

Citation :

Vidyadhar Sharma, Nisha Mathur, "On unified subclass of univalent functions of complex order using the Frasin operator," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 176-179, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P524