Frontiers of Mathematics in China >
Fekete and Szegö problem for a subclass of quasi-convex mappings in several complex variables
Received date: 12 Oct 2014
Accepted date: 10 Dec 2014
Published date: 12 Oct 2015
Copyright
Let be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that , and the estimate is sharp for each λ. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in . The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.
Qinghua XU , Ting YANG , Taishun LIU , Huiming XU . Fekete and Szegö problem for a subclass of quasi-convex mappings in several complex variables[J]. Frontiers of Mathematics in China, 2015 , 10(6) : 1461 -1472 . DOI: 10.1007/s11464-015-0496-5
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