On a class of analytic functions closely related to a class defined by Silverman and Silvia

S.  Kavitha; M.  Darus; S.  Sivasubramanian

doi:10.37863/umzh.v74i11.6523

S. Kavitha SDNB Vaishnav College for Women, Chennai Tamil Nadu, India
M. Darus Univ. Kebangsaan Malaysia, Selangor, Malaysia
S. Sivasubramanian Univ. College of Engineering, Anna Univ., Tindivanam, India

DOI: https://doi.org/10.37863/umzh.v74i11.6523

Keywords: Univalent; Starlike functions of order $\alpha$; Starlike function with respect to a boundary point; Coefficient estimates.

Abstract

UDC 517.5

We define and study a class of analytic functions in the unit disc by using the modification of the well-known Silverman and Silvia's analytic formula for starlike functions with respect to a boundary point. The representation theorem, as well as growth and distortion theorems are established for the new class of functions. Further, early coefficients of the new class of functions are also estimated.

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