Zireh, A., Shabani, M. (2019). On the Linear Combinations of Slanted Half-Plane Harmonic Mappings. Sahand Communications in Mathematical Analysis, 14(1), 89-96. doi: 10.22130/scma.2018.72574.293

Ahmad Zireh; Mohammad Mehdi Shabani. "On the Linear Combinations of Slanted Half-Plane Harmonic Mappings". Sahand Communications in Mathematical Analysis, 14, 1, 2019, 89-96. doi: 10.22130/scma.2018.72574.293

Zireh, A., Shabani, M. (2019). 'On the Linear Combinations of Slanted Half-Plane Harmonic Mappings', Sahand Communications in Mathematical Analysis, 14(1), pp. 89-96. doi: 10.22130/scma.2018.72574.293

Zireh, A., Shabani, M. On the Linear Combinations of Slanted Half-Plane Harmonic Mappings. Sahand Communications in Mathematical Analysis, 2019; 14(1): 89-96. doi: 10.22130/scma.2018.72574.293

On the Linear Combinations of Slanted Half-Plane Harmonic Mappings

^{1}Department of Mathematics, Shahrood University of Technology, P.O.Box 316-36155, Shahrood, Iran.

^{2}Department of Mathematics, Shahrood University of Technology, Shahrood, Iran.

Abstract

In this paper, the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-\gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.