Journal of Applied Analysis 06 (2000), No. 1, 047--075
Copyright Heldermann Verlag 2000
Differential Calculus for Complex-Valued Multifunctions
Jonas Avelin
University College, 80176 Gävle, Sweden
Using the concept of the normal cone to a multifunction we define a derivative for a complex-valued multifunction of one complex variable being a natural generalization of the ordinary complex derivative for holomorphic functions. Using results obtained by Mordukhovich, we develop a full calculus and discuss openness and Lipschitzian properties. We also prove the fundamental theorem of calculus and the Taylor expansion formula. Finally we discuss analyticity of multifunctions in the context of the normal cone.
Keywords: Set-valued function, multifunction calculus, differential calculus, Barrow's theorem, Taylor's theorem, complex-valued multifunction.
MSC: 58C06, 58C20
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