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Differential calculus for complex-valued multifunctions

Avelin J.

Journal of Applied Analysis

2000

Vol. 6, nr 1

47-75

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 obtined 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.