Abstract
Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality ∣Δf(z)∣ ≤ B · ∣Df (z)∣2 for some B > 0 and f(0) = 0. In this note, we show that f does not always satisfy the Schwarz-Pick type inequality
where C(B) is a constant depending only on B. Moreover, a more general Schwarz-Pick type inequality for mapping that satisfies general Poisson differential inequality is established under certain conditions.
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Acknowledgements
The second and third authors would like to express their hearty thanks to the Chern Institute of Mathematics, which provided them with a very comfortable research environment. Also, the authors would like to express their sincere thanks to the referees for their great efforts in improving this paper.
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This research was supported by NNSF of China (11701111), NNSFs of Guangdong Province (2016A030310257 and 2015A030313346) and the Visiting Scholar Program of Chern Institute of Mathematics at Nankai University when the authors worked as visiting scholars.
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Zhong, D., Meng, F. & Yuan, W. On Schwarz-Pick Type Inequality for Mappings Satisfying Poisson Differential Inequality. Acta Math Sci 41, 959–967 (2021). https://doi.org/10.1007/s10473-021-0320-0
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DOI: https://doi.org/10.1007/s10473-021-0320-0