Jinlu Li, Adrian Petrușel, Ching-Feng Wen, Jen-Chih Yao, Covering constants for linear and continuous mappings with applications to stochastic systems of linear equations

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DOI: 10.23952/jnva.11.2027.1.08

Volume 11, Issue 1, 1 February 2027, Pages 155-186

Abstract. Mordukhovich derivatives (Mordukhovich coderivatives) of set-valued mappings in Banach spaces firmly lay the foundation of the theory of generalized differentiation in set-valued analysis, which has been widely applied to varous fields. One of the most important applications of Mordukhovich derivatives is to define the covering constants for set-valued mappings in Banach spaces, which play an important role in Arutyunov Mordukhovich and Zhukovskiy Parameterized Coincidence Point theorem (AMZ theorem). In this paper, we first introduce the concept of locally or globally stochastic systems of linear equations in $\mathbb{R}^n$ . We use the Mordukhovich derivatives to precisely find the covering constants for some linear and continuous mappings in $\mathbb{R}^n$ . In particular, we find the precise solutions of the covering constants for linear and continuous mappings in $\mathbb{R}^2$ and find the exact points, at which the covering constant reaches. Then, by using the AMZ theorem, we prove the existence of solutions to some locally or globally stochastic systems of linear equations in $\mathbb{R}^n$ . Finally, we provide some examples for finding solutions of some stochastic systems of linear equations in $\mathbb{R}^n$ .

How to Cite this Article:
J. Li, A. Petrușel, C.F. Wen, J.C. Yao, Covering constants for linear and continuous mappings with applications to stochastic systems of linear equations, J. Nonlinear Var. Anal. 11 (2027), 155-186.