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Generalized derivatives of a region function and its applications

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Abstract

This paper is based on some fundamental concepts in [7], Clarke's generalized Derivatives[1], as well as Lasotra's and Strauss's definitions of differential D f (x) of a multivalued functionf(x)[6]. Thereby, the generalized derivatives of a region function F(x) is defined as

$$D_F (x) = \cup \cap \left\{ {G(x) \subseteq B(R),} \right.\forall x\varepsilon B(R);\left. {G(x) = F'_x = F'(x)} \right\}$$

The existence of the generalized derivatives of a region function F(x) is discussed; the necessary and sufficient conditions of existence of the Fréchet generalized derivatives of such a function is established.

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References

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Authors and Affiliations

  1. Chongqing Branch of ISTIC, Chongqing

    He Chong

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  1. He Chong
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Communicated by Chien Wei-zang

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Chong, H. Generalized derivatives of a region function and its applications. Appl Math Mech 8, 389–396 (1987). https://doi.org/10.1007/BF02015259

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  • DOI: https://doi.org/10.1007/BF02015259

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