We define and investigate a new subclass of Salagean-type harmonic univalent functions. We obtain coefficient conditions, extreme points, distortion bounds, convolution, and convex combination for the above subclass of harmonic functions.which are analytic in the open unit disk Í {z ∈ : |z| < 1}.We denote the subclass of A consisting of analytic and univalent functions f z in the unit disk Í by S.The following classes of functions and many others are well known and have been studied repeatedly by many authors, namely, Sȃlȃgean 1 , Abdul Halim 2 , and Darus 3 to mention but a few.2 Abstract and Applied Analysis iii δ α {f z ∈ A : Re{f z } > α, 0 ≤ α < 1, z ∈ Í}.

In this paper, a new class of harmonic univalent function using the modified Salagean differential operator is introduced. New results on the new class are obtained. Distortion bounds, Convolution and Convex combination in the new class are also established. The work extended some earlier results .

The study introduced a generalized multiplier operator used as a tool to define and investigate a new class of function, T S Q σ , ξ , ω , ε μ , λ , η ϖ , n and its subclass T S Q σ , ξ , ω , ε μ , λ , η ϖ , n ; M i . Various properties of the class of functions were investigated. The results extend some known results in literature.

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The authors obtained some geometric results on certain new classes of analytic functions involving sigmoid function defined by Fadipe-Joseph et. al. 2016 as T γ (λ, β, α, µ). Extreme point property, radius of starlikeness and convexity, convolution property and Fekete-Szego inequality for the class were proved.