## Abstract

Let's take f(z)=h(z)+g(z)¯ which is an univalent sense-preserving harmonic functions in open unit disc D={z:|z|<1}. If f(z) fulfills |w(z)|=|[Formula presented]|<m, where 0 ≤ m < 1, then f(z) is known m-quasiconformal harmonic function in the unit disc (Kalaj, 2010) [8]. This class is represented by S_{H(m)}. The goal of this study is to introduce certain features of the solution for non-linear partial differential equation f¯_{z¯}=w(z)f(z) when |w(z)| < m, w(z)≺[Formula presented], h(z) ∈ S*(A, B). In such case S*(A, B) is known to be the class for Janowski starlike functions. We will investigate growth theorems, distortion theorems, jacobian bounds and coefficient ineqaulities, convex combination and convolution properties for this subclass.

Original language | English |
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Pages (from-to) | 461-468 |

Number of pages | 8 |

Journal | Applied Mathematics and Computation |

Volume | 319 |

DOIs | |

Publication status | Published - 15 Feb 2018 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2017

## Keywords

- Convex combination
- Convolution properties
- Distortion theorem
- Growth theorem
- Harmonic mapping
- Starlike functions