fixed point theorems in c ∗ -algebra-valued bv(s)-metric spaces with application and numerical methods

We first introduce a novel notion named c ∗ -algebra-valued bv(s)-metric spaces. then, we give proofs of the banach contraction principle, the expansion mapping theorem, and jungck’s theorem in c ∗ - algebra-valued bv(s)-metric spaces. as an application of our results, we establish a result for an integral equation in a c ∗ -algebra-valued bv(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.