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/mjm403/012

Abstract

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(In1γf(z)),(nN0)Inγf(z)=z+k=2(k+γ1+γ)nakzk+(1)nk=1(kγ1+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)zγz2(1+γ)(1z)2,ϕ2(z)=(γ1)zγz2(1+γ)(1z)2
is taken from the article by Yasar and S. Yalçin [1].

Keywords:

Harmonic convex functions

Mathematics Subject Classification:

31A05
  • K. Thilagavathi Department of Mathematics,School of advanced Sciences, VIT University, Vellore-632014, Tamil Nadu, India.
  • K. Vijaya Department of Mathematics,School of advanced Sciences, VIT University, Vellore-632014, Tamil Nadu, India.
  • N. Magesh P.G. and Research Department of Mathematics, Govt Arts College (Men), Krishnagiri - 635 0
  • 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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Published

01-07-2016

How to Cite

K. Thilagavathi, K. Vijaya, and N. Magesh. “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”. Malaya Journal of Matematik, vol. 4, no. 03, July 2016, pp. 443-, doi:10.26637/mjm403/012.