Coefficient inequalities related with typically real functions

Author:

Hussain Saqib1,Khan Shahid2,Noor Khalida Inayat3,Raza Mohsan4

Affiliation:

1. Department of Mathematics , COMSATS University Islamabad , Abbottabad Campus , Abbottabad , Pakistan

2. Department of Mathematics , Riphah International University , Islamabad , Pakistan

3. Department of Mathematics , COMSATS University Islamabad , Islamabad Campus , Islamabad , Pakistan

4. Department of Mathematics , Government College University , Faisalabad , Pakistan

Abstract

Abstract In this paper, we are mainly interested to study the generalization of typically real functions in the unit disk. We study some coefficient inequalities concerning this class of functions. In particular, we find the Zalcman conjecture for generalized typically real functions.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference23 articles.

1. Booth, A.: Researches on the geometrical properties of elliptic integrals, Philos. Trans. Roy. Soc. London 142 (1852), 311–416; 144 (1854), 53–69.

2. Booth, A.: A Treatise on Some New Geometrical Methods, Longmans Green, London, 1877.

3. Fenchel, W.: Bemerkungen über die in Einheitskreis meromorphen schlichten Funktionen, Preuss. Akad. Wiss. Phys. - Math. Kl. 22/23 (1931), 431–436.

4. Goluzin, G. M. On typically real functions, Mat. Sbornik N.S. 27(69) (1950), 201–218 (in Russian).

5. Goodman, W.: Univalent Functions, Vol. I – II, Mariner Publishing Company, Inc., Tampa, Florida, 1983.

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