Abstract
In this paper we give some results concerning Fréchet differentiable mappings between domains in normed spaces with controlled growth. The results are mainly motivated by Pavlović’s equality for the Bloch semi-norm of continuously differentiable mappings in the Bloch class on the unit ball of the Euclidean space as well as the very recent Jocić’s generalization of this result.
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I would like to thank the referee of this paper for carefully reading the paper and pointing out several errors in the first version of the manuscript.
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Marković, M. Representations for the Bloch Type Semi-norm of Fréchet Differentiable Mappings. J Geom Anal 31, 7947–7967 (2021). https://doi.org/10.1007/s12220-020-00559-z
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DOI: https://doi.org/10.1007/s12220-020-00559-z
Keywords
- Bloch functions
- Normal functions
- Operator monotone functions
- Normed spaces
- Banach spaces
- Fréchet differentiable mappings