Corpus ID: 235765463

New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality

  title={New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality},
  author={Serkan cCakmak and Elif Yacsar and Sibel Yalccin},
In this paper, we introduce a new subclass of harmonic functions f = s+ t in the open unit disk U = {z ∈ C : |z| < 1} satisfying Re [ γs′(z) + δzs′′(z) + ( δ−γ 2 ) z2s′′′ (z)− λ ] > ∣∣γt′(z) + δzt′′(z) + ( δ−γ 2 ) z2t′′′ (z) ∣∣ , where 0 ≤ λ < γ ≤ δ, z ∈ U . We determine several properties of this class such as close-to-convexity, coefficient bounds, and growth estimates. We also prove that this class is closed under convex combination and convolution of its members. Furthermore, we investigate… Expand


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