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On T-neighbourhoods of Harmonic Univalent Functions

  • Saman Azizi
  • Ali Ebadian
  • Sibel Yalçin
Research Paper
  • 11 Downloads
Part of the following topical collections:
  1. Mathematics
  2. Mathematics

Abstract

In this present paper, given a sequence \(T=\{T_{n}\}_{n=2}^{\infty }\) consisting of positive numbers, we define the \(T_{\delta }\)-neighbourhood of the function \(f=h+{{\overline{g}}}\in {{\mathcal {H}}}\) is defined as
$$\begin{aligned} N_{\delta }(f)= & {} \left\{ G(z)\;:\;G(z)=z+\sum _{n=2}^{\infty }\left( A_{n}z^{n}+\overline{B_{n}}\overline{z^{n}}\right) ,\right. \\&\;\left. ~\sum _{n=2}^{\infty }T_{n}(|a_{n}-A_{n}|+|b_{n}-B_{n}|)\le \delta ,\;\delta \ge 0\right\} . \end{aligned}$$
Furthermore, we investigate some problems concerning \(T_{\delta }\)-neighbourhoods of functions in various classes of analytic functions. The results obtained here are sharp.

Keywords

Harmonic starlike and convex functions Neighbourhood T-neighbourhood T-factor 

Mathematics Subject Classification

Primary 30C45 

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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of MathematicsPayame Noor UniversityTehranIran
  2. 2.Department of Mathematics, Faculty of SciencesUrmia UniversityUrmiaIran
  3. 3.Department of Mathematics, Faculty of Arts and SciencesBursa Uludag UniversityBursaTurkey

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