Open AccessAuxiliary Principle for a System of Generalized Set-Valued Nonlinear Mixed Variational-Like Inequalities in Banach Spaces
Author(s) -
Yang-Qing Qiu,
Xiaolin Zhan,
Lu-Chuan Ceng
Publication year - 2019
Publication title -
journal of function spaces
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.579
H-Index - 28
eISSN - 2314-8896
pISSN - 2314-8888
DOI - 10.1155/2019/5353748
Subject(s) - banach space , variational inequality , mathematics , convergence (economics) , nonlinear system , iterative method , solution set , set (abstract data type) , regular polygon , pure mathematics , algorithm , discrete mathematics , computer science , geometry , physics , quantum mechanics , economics , programming language , economic growth
In this paper, the auxiliary principle technique is extended to study a system of generalized nonlinear mixed variational-like inequalities problem for set-valued mappings without compact values in Banach spaces with p -uniformly convex bidual spaces. First, the existence of the solutions of the related auxiliary problem is proved. Then, a new iterative algorithm based on the system of auxiliary variational inequalities is constructed. Finally, both the existence of the solutions of the original problem and the convergence of the iterative sequences generated by the algorithm are proved. And we also present a numerical example to demonstrate the result. Our results improve and extend some known results.