Research on Adjoint Kernelled Quasidifferential. (5th March 2014)

• Record Type: Journal Article
• Authors: Lin, Si-Da; Xiao, Fu-Min; Xia, Zun-Quan; Pang, Li-Ping
• Other Names: Ben-El-Mechaiekh Hichem Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-03-05
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/131482
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : The quasidifferential of a quasidifferentiable function in the sense of Demyanov and Rubinov is not uniquely defined. Xia proposed the notion of the kernelled quasidifferential, which is expected to be a representative for the equivalence class of quasidifferentials. Although the kernelled quasidifferential is known to have good algebraic properties and geometric structure, it is still not very convenient for calculating the kernelled quasidifferentials of − f and min f i ∣ i ∈ a finite index set I, where f and f i are kernelled quasidifferentiable functions. In this paper, the notion of adjoint kernelled quasidifferential, which is well-defined for − f and min f i ∣ i ∈ I, is employed as a representative of the equivalence class of quasidifferentials. Some algebraic properties of the adjoint kernelled quasidifferential are given and the existence of the adjoint kernelled quasidifferential is explored by means of the minimal quasidifferential and the Demyanov difference of convex sets. Under some condition, a formula of the adjoint kernelled quasidifferential is presented.