Abstract
In this paper, we enlarge the class of C*-algebra valued partial metric spaces as well as the class of C*-algebra valued b-metric spaces by introducing the class of C*-algebra valued partial b-metric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result in order to examine the existence and uniqueness of a solution for the system of Fredholm integral equations.
Highlights
The theory of fixed point is a very active area of research despite having a history of more than hundred years
The strength of fixed point theory lies in its application, which is spread throughout the existing literature fixed point theory
Several research articles dealing with the fixed point theory for single-valued and multivalued mappings in b-metric spaces and there exists a considerable literature in such spaces
Summary
The theory of fixed point is a very active area of research despite having a history of more than hundred years. With a similar quest, Matthews [3] employed another way to enlarge the class of metric spaces by introducing the notion of partial metric spaces and established an analogue of Banach contraction principle in such spaces. In 2015, Ma et al [23] introduce the notion of C ∗ -algebra valued b-metric spaces as a generalization of C ∗ -avMS and proved some fixed point results used their results as an application for an integral type.
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