Abstract
Rectangular cone b-metric spaces over a Banach algebra are introduced as a generalization of metric space and many of its generalizations. Some fixed point theorems are proved in this space and proper examples are provided to establish the validity and superiority of our results. An application to solution of linear equations is given which illustrates the proper application of the results in spaces over Banach algebra.
Highlights
1 Introduction Liu and Xu in [ ] reported the concept of cone metric space over Banach algebra and proved contraction principles in such space. They replaced the usual real contraction constant with a vector constant and scalar multiplication with vector multiplication in their results and furnished proper examples to show that their results were different from those in cone metric space and metric space
The concept defined by Liu and Xu [ ] was further generalized by Huang and Radenovic [ ] by the introduction of a cone b-metric space over a Banach algebra
In this paper we have introduced the concept of a rectangular cone b-metric space over a Banach algebra and proved the Banach contraction principle and weak Kannan contraction principle in this space
Summary
Reny George[1,2], Hossam A Nabwey[1,3], R Rajagopalan[1], Stojan Radenovic4,5* and KP Reshma[6]
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