Abstract
The concept of C^{∗}-algebra-valued rectangular b-metric spaces is introduced as a generalization of C^{∗}-algebra-valued b-metric spaces. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. As applications, existence and uniqueness results for a type of operator equation is given.
Highlights
It is well known that the Banach contraction mapping principle is a very useful, simple and classical tool in modern analysis and it has many applications in applied mathematics
The concept of C -algebra-valued rectangular b-metric spaces is introduced as a generalization of C -algebra-valued b-metric spaces
In [8], Ma established the notion of C -algebra-valued metric spaces and proved some ...xed point theorems for self maps with contractive or expansive mappings
Summary
It is well known that the Banach contraction mapping principle is a very useful, simple and classical tool in modern analysis and it has many applications in applied mathematics. Czerwik [4] extended the results of b-metric spaces Using this idea many researcher presented generalization of the renowned Banach ...xed point theorem in the b-metric spaces. C -algebra; C -algebra-valued rectangular b-metric spaces, contractive mapping, ...xed point theorem. In [8], Ma established the notion of C -algebra-valued metric spaces and proved some ...xed point theorems for self maps with contractive or expansive mappings. Kamran et al [7] proved the Banach contraction principle in C -algebra-valued b-metric spaces with application. In [5], Meltem and Alaca presented the concept of C -algebra-valued S-metric spaces and proved Banach contraction principle in such spaces. We introduce the new type of metric spaces namely C -algebravalued rectangular b-metric spaces and we give some ...xed point theorems for self maps with contractive conditions. Existence and uniqueness results for a type of operator equation is given
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