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
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.26658
  • Analytic function, Starlike function, Convex function, Quasi-subordination, Log-Sigmoid function, kth root transformation

  • 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. [1] Ali,R.M., Lee.S.K., Ravichandran. and Supramaniam,S ., “The Fekete –Szegö coefficient functional for transforms of analytic functionsâ€, Bulletin of the Iranian Mathematical Society, Vol. 35 No. 2, (2009), pp: 119-142.

      [2] Annamalia.S, Ramachandran.C and Murugusundaramoorthy, “Fekete- Szegö coefficient for the Janowski -spirallike function in open unit discâ€, International Journal of Mathematical Analysis, Vol.8, No.19, (2012), pp: 913-918.

      [3] Babalola.K.O (@013), “On pseudo starlike functionsâ€, Journal of Classical Analysis, Vol.3, No.2, pp: 137-147.

      [4] Duren.P.l, “Univalent Functionsâ€, Grundlehren der Mathematischen Wissenchaften, Vol.259, (1983) , Springer, New York.

      [5] Faipe-Joseph.O.A, Oladipo.A.T. Ezeafulukwe.U.A. (2013), Modified 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 functionâ€, Journal of London Mathematical Society, Vol.8, (1933), pp:85-89.

      [7] Hamzat Jamiu Olusegun , “Coefficient bounds for bazilevic functions 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 functionsâ€, Proceedings of the American Mathematical Society, Vol.20, (1969), pp:8-12.

      [9] Murugusundarmoorthy.G and Janani.T, “Sigmoid function in the space of univalent -pseudo starlike functionsâ€, 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-subordinationâ€, Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, Vol.16, (2017), pp :7-15.

      [11] Najla.M, Alarifi and Maisarah Haji Mohd, “Best bounds of the second Hankel determinants of the kth root transform of analytic functionsâ€, AIP Conference Proceedings, Vol.1682, No.2, (2015).

      [12] Nehari.Z, “Conformal Mappingâ€, 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 typeâ€, Scientia 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 functionsâ€, Journal 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 functionsâ€, 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 conjectureâ€, 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 functions subordinate to a shell shaped regionâ€, The Journal of Analysis, Vol.25, (2016), pp: 93-105.

      [19] Singh.R.(1973), “ On Bazilevic functionsâ€, 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 coefficientsâ€, 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 transformations for a subclass of p-valent functionsâ€, Bulletin of Calcutta Mathematical Society, Vol.107, No.4, .(2015), pp: 291-304.

      [22] Sunday Olufemi Olantunji and Emmanuel Jesuyon Dansu, “Coefficient estimates for Bazilevic Ma-Minda functions in the space of sigmoid functionsâ€, Malaysian Journal of Mathematik, Vol.4, No.3, (2016), pp: 505-512.

      [23] Vamshee Krishna.D, Venkateshwarlu.B, and Ram Reddy.T, “Coefficient inequality for transforms of reciprocal of bounded turning functionsâ€, 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.

  • Downloads

  • 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 & Technology, 7(4.10), 1007-1011. https://doi.org/10.14419/ijet.v7i4.10.26658