Kth Root Transformation for a subclass of Log-Sigmoid Analytic Function based on Quasi-Subordination

  • Authors

    • M. Hari Priya
    • R. Bharavi Sharma
    • V. Suman Kumar
    https://doi.org/10.14419/ijet.v7i4.10.26658

    Received date: January 29, 2019

    Accepted date: January 29, 2019

    Published date: October 2, 2018

  • Analytic function, Starlike function, Convex function, Quasi-subordination, Log-Sigmoid function, kth root transformation

  • Abstract

    In the present investigation, using the concept of quasi-subordination, two subclasses of analytic functions have been introduced. The coefficient inequalities, the Fekete-Szego inequality, upper bounds for kth  root transformation were studied. This study is extended to function  and for  .

  • References

    1. Ali,R.M., Lee.S.K., Ravichandran. and Supramaniam,S ., “The Fe-kete –Szegö coefficient functional for transforms of analytic functions”, Bulletin of the Iranian Mathematical Society, Vol. 35 No. 2, (2009), pp: 119-142.
    2. Annamalia.S, Ramachandran.C and Murugusundaramoorthy, “Fe-kete- Szegö coefficient for the Janowski -spirallike function in open unit disc”, International Journal of Mathematical Analysis, Vol.8, No.19, (2012), pp: 913-918.
    3. Babalola.K.O (@013), “On pseudo starlike functions”, Journal of Classical Analysis, Vol.3, No.2, pp: 137-147.
    4. Duren.P.l, “Univalent Functions”, Grundlehren der Mathematischen Wissenchaften, Vol.259, (1983) , Springer, New York.
    5. Faipe-Joseph.O.A, Oladipo.A.T. Ezeafulukwe.U.A. (2013), Modi-fied sigmoid function in univalent function theory, International Journal of Mathematical Sciences and Engineering Application, Vol.7,No.7, pp:313-317.
    6. Fekete.M and Szego.G), “Eine Bermerkung uber ungerade schlichte function”, Journal of London Mathematical Society, Vol.8, (1933), pp:85-89.
    7. Hamzat Jamiu Olusegun , “Coefficient bounds for bazilevic func-tions associated with modified sigmoid functions, Asian Research Journal of Mathematics, Vol.5, No.3, (2017), pp: 1-10.
    8. Keogh.F.R and Merkes.E.P., “A coefficient inequality for certain classes of analytic functions”, Proceedings of the American Mathe-matical Society, Vol.20, (1969), pp:8-12.
    9. Murugusundarmoorthy.G and Janani.T, “Sigmoid function in the space of univalent -pseudo starlike functions”, International Journal of Pure and Applied Mathematics, Vol.101, No.1, (2015), pp : 33-41.
    10. Nanjundan Magesh, Jagadeesan Yamini, “Fekete-Szego inequalities associated with k-th root transformation based on quasi-subordination”, Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, Vol.16, (2017), pp :7-15.
    11. Najla.M, Alarifi and Maisarah Haji Mohd, “Best bounds of the sec-ond Hankel determinants of the kth root transform of analytic func-tions”, AIP Conference Proceedings, Vol.1682, No.2, (2015).
    12. Nehari.Z, “Conformal Mapping”, McGraw-Hill, New York, NY,USA, 1st Edition, .(1952).
    13. Olatunji.A.O, Gbolagde. M, Anake.T and Fadipe-Joseph. “Sigmoid function in the space of univalent function of Bazelevic type”, Sci-entia Magna, Vol.97, No.3, (2013), pp :43-51.
    14. Olantunji.A.O, “Sigmoid function in the space of univalent pseudo starlike function with Sakaguchi type functions”, Jour-nal of Progressive Research in Mathematics (JPRM), Vol.7, No.4, pp: 1164-1172.
    15. Olantunji.S.O., Dansu.E.J and 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 Application, Vol.5, No.1, (2017), pp :97-105.
    16. Pommernke.C.(1966), On the coefficients and Hankel determinants of univalent functions, Journal of London Mathematical Society, Vol.41, pp: 111-122.
    17. Robertson.M.S., “Quasi-Subordination and coefficient conjecture”, Bulletin of the American Mathematical Society, Vol.76, .(1970) pp: 1-9.
    18. Sharma.R.B, and Hari Priya.M, “On a class of convex func-tions subordinate to a shell shaped region”, The Journal of Analysis, Vol.25, (2016), pp: 93-105.
    19. Singh.R.(1973), “ On Bazilevic functions”, Proceedings of the American Mathematical Society, Vol.28, pp: 261-271.
    20. Sharma.R.B. and Tam Reddy.T and Saroja.K, “A new subclass of Meromorphic functions with positive coefficients”, Indian Journal of Pure and Applied Mathematics, Vol.44, No.1, .(2013).
    21. Sharma.R.B. and Tam Reddy.T and Hari Priya.M., “Kth root trans-formations for a subclass of p-valent functions”, Bulletin of Calcut-ta Mathematical Society, Vol.107, No.4, .(2015), pp: 291-304.
    22. Sunday Olufemi Olantunji and Emmanuel Jesuyon Dansu, “Coeffi-cient estimates for Bazilevic Ma-Minda functions in the space of sigmoid functions”, Malaysian Journal of Mathematik, Vol.4, No.3, (2016), pp: 505-512.
    23. Vamshee Krishna.D, Venkateshwarlu.B, and Ram Reddy.T, “Coef-ficient inequality for transforms of reciprocal of bounded turning functions”, Annales Univ.Sci. Budapest., Sect.Comp., Vol.44, (2015), pp: 69-77.
    24. Vamshee Krishna.D, Venkateshwarlu.B, Hankel determinant for transforms of pre-starlike functions of order alpha, South-East Asian Bulletin of Mathematics, Vol.40, (2016), pp: 131-140.

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  • How to Cite

    Hari Priya, M., Bharavi Sharma, R., & Suman Kumar, V. (2018). Kth Root Transformation for a subclass of Log-Sigmoid Analytic Function based on Quasi-Subordination. International Journal of Engineering and Technology, 7(4.10), 1007-1011. https://doi.org/10.14419/ijet.v7i4.10.26658