Generalized Derivatives of a Region Function and Its Applications

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He Chong. Generalized Derivatives of a Region Function and Its Applications[J]. Applied Mathematics and Mechanics, 1987, 8(4): 377-384.

Citation:

He Chong. Generalized Derivatives of a Region Function and Its Applications[J]. Applied Mathematics and Mechanics, 1987, 8(4): 377-384.

Citation:

He Chong. Generalized Derivatives of a Region Function and Its Applications[J]. Applied Mathematics and Mechanics, 1987, 8(4): 377-384.

Abstract

This paper is based on tome fundamental concepts in [7], Clarke's generalized derivatives[1], as well as Lasotra's and Strauss's definitions of differential D(x) of a multivalued function f(x)[6]. Thereby, the generalized derivatives of a region function f(x) is defined as D_F=∪∩{G(x)⊆B(R),∀x∈B(R);G(x)=F_x=F(x)} The existence of the generalized derivatives of a region function F(x) is discussed; the necessary and sufficient conditions of existence of the Frechet generalized derivatives of such a function is established.

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