Erratum: Certain properties of a subclass of harmonic convex functions of complex order defined by multiplier transformations-Malaya J. Mat. 4(3)2016, 362-372
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DOI:
https://doi.org/10.26637/mjm403/012Abstract
In the paper entitled Certain properties of a subclass of harmonic convex functions of complex order defined by Multiplier transformations- Malaya J. Mat. 4(3)2016, 362-372, the presentation of definition of modified Multiplier transformation of harmonic function f=h+ˉg as given below.
I0γf(z)=D0f(z)=h(z)+¯g(z)I1γf(z)=γD0f(z)+D1f(z)γ+1Inγf(z)=I1γ(In−1γf(z)),(n∈N0)Inγf(z)=z+∞∑k=2(k+γ1+γ)nakzk+(−1)n∞∑k=1(k−γ1+γ)nbkzk
Also if f is given, then,
Inγf(z)=f˜∗(ϕ1(z)+¯ϕ2(z))~……∗(ϕ1(z)+¯ϕ2(z))⏟n− times =h∗(ϕ1(z)∗…(ϕ1(z)⏟n− times +¯g+(ϕ2(z)∗…(ϕ2(z)))⏟n− times ,
where ∗ denotes the usual Hadamard product or convolution of power series and
ϕ1(z)=(1+γ)z−γz2(1+γ)(1−z)2,ϕ2(z)=(γ−1)z−γz2(1+γ)(1−z)2
is taken from the article by Yasar and S. Yalçin [1].
Keywords:
Harmonic convex functionsMathematics Subject Classification:
31A05- Pages: 443-443
- Date Published: 01-07-2016
- Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)
E. Yasar and S. Yalc ¸in, Certain properties of a subclass of harmonic functions, Appl. Math. Inf. Sci., 7(5)(2013), 1749-1753. DOI: https://doi.org/10.12785/amis/070512
- NA
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