The Univalent Function Created by the Meromorphic Functions Where Defined on the Period Lattice

Year 2019, Volume: 2 Issue: 4, 303 - 308, 29.12.2019

Hasan Sahin , İsmet Yıldız

https://doi.org/10.33434/cams.607382

Abstract

The function $ \xi(z)$ is obtained from the logarithmic derivative function  $\sigma(z)$. The elliptic function $ \wp(z) $ is also derived from the $ \xi(z) $ function. The function $ \wp(z) $ is a function of double periodic and meromorphic function on lattices region. The function $ \wp(z) $ is also double function. The function $ \varphi(z) $  meromorphic and univalent function  was obtained  by the serial expansion of the function $ \wp(z)$. The function $ \varphi(z) $ obtained here is shown to be a convex function.

Keywords

Convex function, Elliptic function, Latices, Meromorphic function

References

• [1] M. Dutta, L. Debnath, Elements of the Elliptic and Associated Functions with Application, Calcutta, 1965.
• [2] A. W. Goodman, Univalent Functions, Florida, 1983.
• [3] P. L. Duren, Univalent Functions, Springer-Verlag, New York, 1983.