Based on the concept and properties of C * -algebras, the paper introduces a concept of C * -algebra-valued metric spaces and gives some fixed point theorems for self-maps with contractive or expansive conditions on such spaces. As applications, existence and uniqueness results for a type of integral equation and operator equation are given. MSC: 47H10; 46L07
Based on the concept and properties of C * -algebras, the paper introduces a concept of C * -algebra-valued b-metric spaces which generalizes the concept of C * -algebra-valued metric spaces and gives some basic fixed point theorems for self-map with contractive condition on such spaces. As applications, existence and uniqueness results for a type of operator equation and an integral equation are given.
MSC: 47H10; 46L07
Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and \documentclass[12pt]{minimal}\begin{document}${\mathbb {C}}G$\end{document}CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra \documentclass[12pt]{minimal}\begin{document}${\mathcal {F}}_H$\end{document}FH of the field algebra \documentclass[12pt]{minimal}\begin{document}$\mathcal {F}$\end{document}F of G-spin models, so that \documentclass[12pt]{minimal}\begin{document}${\mathcal {F}}_H$\end{document}FH is a D(H; G)-module algebra, whereas \documentclass[12pt]{minimal}\begin{document}$\mathcal {F}$\end{document}F is not. Then the observable algebra \documentclass[12pt]{minimal}\begin{document}${\mathcal {A}}_{(H,G)}$\end{document}A(H,G) is obtained as the D(H; G)-invariant subalgebra of \documentclass[12pt]{minimal}\begin{document}${\mathcal {F}}_H$\end{document}FH, and there exists a unique C*-representation of D(H; G) such that D(H; G) and \documentclass[12pt]{minimal}\begin{document}${\mathcal {A}}_{(H,G)}$\end{document}A(H,G) are commutants with each other.
In this paper, we establish coincidence fixed point and common fixed point theorems for two mappings in complete C * -algebra-valued metric spaces which satisfy new contractive conditions. Some applications of our obtained results are given. c 2016 all rights reserved.
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