ON A COMPREHENSIVE CLASS OF ANALYTIC P-VALENT FUNCTIONS ASSOCIATED WITH SHELL-LIKE CURVE AND MODIFIED SIGMOID FUNCTION

Abstract

In this paper, the authors introduce and study a new class of analytic p-valent functions and its connections with some famous subclasses of analytic and univalent functions associated with shell-like curve and modified sigmoid function in the open unit disk E= {z : z |<1}. In particular, the coefficient condition for function f(z) belonging to the class Bp (λ, β) is investigated using a succinct mathematical approach. In addition, as a special case, convex functions of order 1/4 are shown to be in the aforementioned class Bp(λ, β) in E. With the aid of subordination principle, the authors obtain the first three Taylor-Maclaurin coefficients |ap+1 | , |ap+2 | and |ap+3 | as well as the Fekete-Szegö functional |ap+2 -ηa2p+1| for functions f(z) belonging to the class Bp(λ, β, σ;p ̃) involving modified sigmoid function and associated with shell-like curve.