LINEAR COMBINATIONS OF UNIVALENT HARMONIC MAPPINGS WITH COMPLEX COEFFICIENTS

Authors

  • D. Khurana Department of Mathematics, Hans Raj Mahila Maha Vidyalaya, Jalandhar-144008, India Author
  • R. Kumar Department of Mathematics, DAV University, Jalandhar-144012, India Author
  • S. Gupta Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148106, India Author
  • S. Singh Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148106, India Author

Keywords:

Univalent harmonic mappings, linear combination, convex in the horizontal direction

Subjects:

30C45

Abstract

We study the linear combinations $f(z)= \lambda f_{1}(z)+(1-\lambda) f_{2}(z)$ of two univalent harmonic mappings $f_{1}$ and $f_{2}$ in the cases when $\lambda$ is some complex number. We determine the radius of close-to-convexity of $f$ and establish some sufficient conditions for $f$ to be locally-univalent and sense-preserving. Some known results reduce to particular cases of our general results.

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Published

2022-07-15

Issue

Vol. 74 No. 3 (2022): Vol. 74, Issue 3

Section

Articles

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This work is licensed under a Creative Commons Attribution 4.0 International License.