Abstract
In this paper we first study the relationship between local and global Minty-Browder monotone operators and then we show that these operators have generally convex preimages. Our results allow to show that positive semidefinitedness on the complement of a discrete set of the differential operator implies the Minty-Browder monotonicity of the operator itself. We also show that complex functions of one complex variable are Minty-Browder monotone under suitable conditions. Finally, we obtain some injectivity/univalency theorems that generalize some well-known results.
Citation
Gábor Kassay. Cornel Pintea. Ferenc Szenkovits. "ON CONVEXITY OF PREIMAGES OF MONOTONE OPERATORS." Taiwanese J. Math. 13 (2B) 675 - 686, 2009. https://doi.org/10.11650/twjm/1500405394
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