Some Results of New Subclasses for Bi-Univalent Functions Using Quasi-Subordination
Waggas Galib Atshan, Ibtihal Abdul Ridha Rahman, Alina Alb Lupaş
Abstract
In this paper, we introduce new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ of bi-univalent functions in the open unit disk U by using quasi-subordination conditions and determine estimates of the coefficients a2 and a3 for functions of these subclasses. We discuss the improved results for the associated classes involving many of the new and well-known consequences. We notice that there is symmetry in the results obtained for the new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ, as there is a symmetry for the estimations of the coefficients a2 and a3 for all the subclasses defind in our this paper.
Topics & Concepts
Subordination (linguistics)Unit diskSymmetry (geometry)Unit (ring theory)MathematicsPure mathematicsNoticeUnivalent functionCombinatoricsDiscrete mathematicsAnalytic functionGeometryLawPhilosophyPolitical scienceMathematics educationLinguisticsAnalytic and geometric function theoryCrystal Structures and PropertiesX-ray Diffraction in Crystallography