ON A COMPREHENSIVE CLASS OF ANALYTIC P-VALENT FUNCTIONS ASSOCIATED WITH SHELL-LIKE CURVE AND MODIFIED SIGMOID FUNCTION
Jamiu Olusegun Hamzat1* and Abiodun Tinuoye Oladipo2
1Department of Mathematics, Faculty of Science, University of Lagos, Nigeria.
2Department of Pure and Applied Mathematics, Faculty of Pure and Applied Sciences,
Ladoke Akintola University of Technology, Ogbomoso Oyo State, Nigeria.
1* This email address is being protected from spambots. You need JavaScript enabled to view it., 2This email address is being protected from spambots. You need JavaScript enabled to view it.
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.
Keywords: Analytic Function, Bounded Turning Function, Convex Function, Starlike Function, Univalent Function.
Published On: 14 February 2022
