Abstract
In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate these results.
Highlights
Fixed points theory has become an important field in mathematics due to its variety of applications in science, economics and game theory
In 2015, George et al [4] introduced the notion of rectangular b-metric space as a generalization of rectangular metric space and they presented some fixed point results for contractive mappings
We introduce the notion of extended rectangular b-metric spaces which is a combination of properties of rectangular metric spaces and extended b-metric spaces
Summary
Fixed points theory has become an important field in mathematics due to its variety of applications in science, economics and game theory. Brouwer’s fixed-point theorem states that any continuous mapping on a compact convex set to itself has a fixed point. In addition to their importance in differential and integral equations, Brouwer’s theorem and its extension Kakutani theorem for set valued function play a very important role in proving the existence of general equilibrium in market economics and the existence of Nash equilibria in game theory—for more details, see [1,2]. In 2015, George et al [4] introduced the notion of rectangular b-metric space as a generalization of rectangular metric space and they presented some fixed point results for contractive mappings.
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