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Differential Calculus for Complex-Valued Multifunctions
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J. Avelin
Published/Copyright:
June 4, 2010
Abstract
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.
Key words and phrases.: Set-valued function; multifunction calculus; differential calculus; Barrow's theorem; Taylor's theorem; complex-valud
Received: 1998-05-05
Revised: 1999-06-17
Published Online: 2010-06-04
Published in Print: 2000-June
© Heldermann Verlag
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Keywords for this article
Set-valued function;
multifunction calculus;
differential calculus;
Barrow's theorem;
Taylor's theorem;
complex-valud
Articles in the same Issue
- Feynman's Path Integrals and Henstock's Non-Absolute Integration
- Universally Polygonally Approximable Functions
- Differential Calculus for Complex-Valued Multifunctions
- On Analogues of Some Classical Subsets of the Real Line
- Oscillation Criteria of Comparison Type for Second Order Difference Equations
- On the Convergence of the Method of Lines for Quasi–Nonlinear Functional Evolutions in Banach Spaces
- Bounded Solutions for Nonlinear Elliptic Equations in Unbounded Domains
- A Characterization of Strict Local Minimizers of Order One for Static Minmax Problems in the Parametric Constraint Case
- On Linear Dependence of Iterates
