Relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{\mu }$$\end{document}-quasimonotone variational inequalities in Hadamard manifolds

被引：0
作者：
Alireza Amini-Hararandi
Majid Fakhar
Laleh Nasiri
机构：
[1] University of Isfahan,Department of Mathematics
来源：
Journal of Fixed Point Theory and Applications | 2019年 / 21卷 / 3期
关键词：
Hadamard manifold; variational inequality; relaxed ; -quasimonotone; relaxed ; -quasiconvex; Primary 49J40; Secondary 58E35; 47H04;
D O I：
10.1007/s11784-019-0724-9
中图分类号：
学科分类号：
摘要：
In this article, we introduce relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasimonotone set-valued vector field on Hadamard manifolds and prove the existence of solutions of the Stampacchia variational inequality for such mappings. We also present the notion of relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasiconvexity and show that the Upper Dini and Clarke–Rockafellar subdifferentials of a relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasiconvex function is relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasimonotone. Under relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasiconvexity in the nondifferentiable sense, we establish the connection between the Stampacchia variational inequality problem and a nonsmooth constrained optimization problem.
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