Abstract
In this paper, we prove some common fixed point theorems for rational contraction mapping on complex partial b -metric space. The presented results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results.
Highlights
Introduced in 1989 by Bakhtin [1] and Czerwick [2], the concept of b-metric spaces provided a framework to extend the results already known in the classical setting of metric spaces
In 2017, Dhivya and Marudai [5] introduced the concept of complex partial metric space and suggested a plan to expand the results, as well as proved common fixed point theorems under the rational expression contraction condition
We prove some common fixed point theorems for rational contraction mapping on complex partial b-metric space
Summary
Introduced in 1989 by Bakhtin [1] and Czerwick [2], the concept of b-metric spaces provided a framework to extend the results already known in the classical setting of metric spaces. The concept of complex valued metric spaces was introduced in 2011 by Azam et al [3] and given some common fixed point theorems under the condition of contraction. Rao et al [4] introduced the definition of complex valued b -metric spaces in 2013 and provided a scheme to expand the results, as well as proved a common fixed point theorem under contraction. In 2017, Dhivya and Marudai [5] introduced the concept of complex partial metric space and suggested a plan to expand the results, as well as proved common fixed point theorems under the rational expression contraction condition. Gunaseelan [6, 7] presented the concept of complex partial b-metric space in 2019, as well as proved the fixed point theorem under the contractive condition. We prove some common fixed point theorems for rational contraction mapping on complex partial b-metric space
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