2 results
Improved Bloch and Landau constants for meromorphic functions
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 66 / Issue 4 / December 2023
- Published online by Cambridge University Press:
- 28 April 2023, pp. 1269-1273
- Print publication:
- December 2023
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- Article
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Let
${\mathbb D}$ be the open unit disk, and let 
$\mathcal {A}(p)$ be the class of functions f that are holomorphic in 
${\mathbb D}\backslash \{p\}$ with a simple pole at 
$z=p\in (0,1)$, and 
$f'(0)\neq 0$. In this article, we significantly improve lower bounds of the Bloch and the Landau constants for functions in 
${\mathcal A}(p)$ which were obtained in Bhowmik and Sen (2023, Monatshefte für Mathematik, 201, 359–373) and conjecture on the exact values of such constants.
RADII OF HARMONIC MAPPINGS IN THE PLANE
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 102 / Issue 3 / June 2017
- Published online by Cambridge University Press:
- 08 July 2016, pp. 331-347
- Print publication:
- June 2017
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In this paper, for the convolution and convex combination of harmonic mappings, the radii of univalence, full convexity and starlikeness of order
$\unicode[STIX]{x1D6FC}$ are explored. All results are sharp. By way of application, the univalent radius and the Bloch constant of the convolution of two bounded harmonic mappings are obtained.
