Abstract
Abstract 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.
Highlights
We begin with the concept of C∗-algebras.Suppose that A is a unital algebra with the unit I
In, Huang and Zhang [ ] introduced the concept of cone metric space, replacing the set of real numbers by an ordered Banach space. Many authors generalized their fixed point theorems on different type of metric spaces [ – ]
In [ ], the authors studied the operator-valued metric spaces and gave some fixed point theorems on the spaces
Summary
We begin with the concept of C∗-algebras.Suppose that A is a unital algebra with the unit I. Many authors generalized their fixed point theorems on different type of metric spaces [ – ]. In [ ], the authors studied the operator-valued metric spaces and gave some fixed point theorems on the spaces. We introduce a new type of metric spaces which generalize the concepts of metric spaces and operator-valued metric spaces, and give some related fixed point theorems for self-maps with contractive or expansive conditions on such spaces.
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