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IJET International Journal of Engineering and Technology E-ISSN 2227-524X

On Certain New Subclass of Sakaguchi Type Function Related to Sigmoid Functions

Abstract

The object of the present paper is to obtain initial coefficients | |,| |,| |, upper bounds of | | and second Hankel determinant associated with a class of analytic univalent function of sakaguchi  type function related to sigmoid function in the open unit disc ∆. Various authors as Abiodum, Tinuoye Oladipo, Murugusundaramoorthy et. al., and Olatunji have studied sigmoid function for different classes of analytic and univalent functions. Our results serves as a generalisation in this direction and it gives birth some existing subclasses of functions.

Authors and Affiliations

  • B. Srutha Keerthi
  • M. Revathi

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Keywords

  • coefficient estimate
  • Analytic function
  • univalent function
  • Starlike function
  • convex functionsubordination
  • upper bound
  • sigmoid function
  • differential operator
  • second Hankel determinant.

References

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[3] Fadipe-Joseph, OA, Oladipo, AT & Ezeafulukwe, UA, “Modified sigmoid function in univalent function theory”, International Journal of Mathematical Sciences and Engineering Application, Vol.7, No.7, (2013), pp.313-317.

[4] Murugusundaramoorthy G & Janani T, “Sigmoid Function in the Space of Univalent $Lambda $-Pseudo Starlike Functions”, International Journal of Pure and Applied Mathematics, Vol.101, No.1, (2015), pp.33-41.

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View more references (5)

[6] Oladipo AT, “Coefficient inequality for subclass of analytic univalent functions related to simple logistic activation functions”, Stud. Univ. Babes-Bolyai Math, Vol.61, (2016), pp.45-52

[7] Olatunji SO, “Sigmoid function in the space of univalent lambda pseudo starlike function with Sakaguchi type functions”, Journal of Progressive Research in Mathematics, Vol.7, No.4, (2016), pp.1164-1172.

[8] Olatunji S, Dansu E & Abidemi A, “On a sakaguchi type class of analytic functions associated with quasi-subordination in the space of modified sigmoid functions”, Electronic Journal of Mathematical Analysis and Applications, Vol.5, No.1, (2017), pp.97-105.

[9] Sakar FM, Aytas S & Guney O, “On the Fekete-Szeg¨ o problem for a generalised class defined by differential operator”, Suleyman Derminal University Journal of Natural and Applied Sciences, Vol.20, No.3, (2016), pp.456-459.

[10] Sahsene A, “Application of Quasi-Subordination for generalised Sakaguchi type functions”, Journal of Complex Analysis, (2017).


How to Cite

Srutha Keerthi, B., & Revathi, M. (2018). On Certain New Subclass of Sakaguchi Type Function Related to Sigmoid Functions. International Journal of Engineering and Technology, 7(4.36), 766-768. https://doi.org/10.14419/ijet.v7i4.36.24238