Systems of Generalized Quasivariational Inclusion Problems with Applications in <inline-formula> <graphic file="1687-1812-2011-561573-i1.gif"/></inline-formula>-Spaces

• Main Authors: Xu Jiu-ping, Yang Ming-ge, Huang Nan-jing
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Fixed Point Theory and Applications
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2011/561573

<p/> <p>We first prove that the product of a family of <inline-formula> <graphic file="1687-1812-2011-561573-i2.gif"/></inline-formula>-spaces is also an <inline-formula> <graphic file="1687-1812-2011-561573-i3.gif"/></inline-formula>-space. Then, by using a Himmelberg type fixed point theorem in <inline-formula> <graphic file="1687-1812-2011-561573-i4.gif"/></inline-formula>-spaces, we establish existence theorems of solutions for systems of generalized quasivariational inclusion problems, systems of variational equations, and systems of generalized quasiequilibrium problems in <inline-formula> <graphic file="1687-1812-2011-561573-i5.gif"/></inline-formula>-spaces. Applications of the existence theorem of solutions for systems of generalized quasiequilibrium problems to optimization problems are given in <inline-formula> <graphic file="1687-1812-2011-561573-i6.gif"/></inline-formula>-spaces.</p>