SOME RESULTS ON A SUBCLASS OF HARMONIC MAPPINGS OF ORDER ALPHA

Abstract

Let SH be the class of harmonic mappings defined by SH = { f = h z + g z | h z = z + ∑∞ n=2 anz n , g z = b1z + ∑∞ n=2 bnz n , b1 < 1 } where h z and g z are analytic. Additionally f z ∈ SH α ⇔     zh′ z − zg′ z h z + g z − 1 − b1 1 + b1 < 1 − b1 1 + b1  − α, z ∈ U, 0 6 α < 1 − b1 1 + b1 In the present work, by considering the analyticity of the functions defined by R. M. Robinson [7], we discuss the applications to the harmonic mappings.

Keywords

• Harmonic Mappings,Subordination principle,Distortion theorem

References

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