A New Subclass of Univalent Functions Connected with Convolution defined via employing a Linear combination of two generalized Differential operators involving Sigmoid Function

Year 2020, Issue: 2, 82 - 96, 12.11.2020

Ezekiel Abiodun Oyekan , Ibrahim Awolere

https://doi.org/10.47087/mjm.791841

Cited By: 2

Abstract

By introducing an operator E_μ^n (β,λ,ω,φ;t) f_γ (z) via a linear combination of two generalized differential operators involving modified Sigmoid function, we defined and studied certain geometric properties of a new subclass T_γ D_(λ,ω) (α,β,ω,φ,t,λ,η,ξ;p:n) of analytic functions in the open unit disk $U.$ In particular, we give some properties of functions in this subclass such as; coefficient estimates, growth and distortion theorems, closure theorem and Fekete-Szego ̌ inequality for functions belonging to the subclass. Some earlier known results are special cases of results established for the new subclass defined.

Keywords

Analytic function , convolution , Fekete-Szego inequality , growth and distortion , Sigmoid function

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