Early Coefficient Bounds and Fekete–Szegö Inequality for a Subclass of Analytic Functions Defined by a New Generalized Differential Operator

Abstract

In this paper, a new subclass, E_(ψ,κ,τ) (σ,λ,μ,α,β,δ,η,l,t) of analytic functions, defined through a new generalized differential operator D_(μ,λ,σ)^m (α,β,δ,η,l,t) and the Janowski function is introduced and analyzed. The subclass E_(ψ,κ,τ) (σ,λ,μ,α,β,δ,η,l,t), is constructed via subordination involving a linear combination of the operator and its derivatives. For this class, sharp bounds for the initial coefficients |a_2 | and |a_3 | were established and a precise form of the Fekete–Szegö inequality derived.