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

Authors and Affiliations

  • B. Srutha Keerthi
  • M. Revathi

About this article

DOI:

https://doi.org/10.14419/ijet.v7i4.36.24238

Download PDF

Keywords:

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

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.

References

Ali RM, Ravichandran V & Seenivasagan N, “Coefficient bounds for p-valent functions”, Applied Mathematics and Computation, Vol.187, No.1, (2007), pp.35-46.

Ali RM, Ravichandran V & Lee SK, “Subclasses of multivalent starlike and convex functions”, Bulletin of the Belgian Mathematical Society-Simon Stevin, Vol.16, No.3, (2009), pp.385-394.

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.

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.

Noonan JW & Thomas DK, “On the second Hankel determinant of areally mean p-valent functions”, Transactions of the American Mathematical Society, Vol.223, (1976), pp.337-346

View more references (5)

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

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.

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.

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.

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

Downloads