Fixed Point Theorems in C*-Algebra-Valued bu(s)-Metric Spaces with Application and Numerical Methods

We first introduce a novel notion named C*-algebra-valued bu(s)-metric spaces. Then, we give proofs of the Banach contraction principle, the expansion mapping theorem, and Jungck's theorem in C*algebra-valued bu(s)-metric spaces. As an application of our results, we establish a result for an integral equation in a C*-algebra-valued bu(s)metric space. Finally, a numerical method is presented to solve the proposed integral equation, and the convergence of this method is also studied. Moreover, a numerical example is given to show applicability and accuracy of the numerical method and guarantee the theoretical results.