The aim of this work is to usher in a tripled $b$-metric spaces, triple weakly $\alpha_s$-admissible, triangular partially triple weakly $\alpha_s$-admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, We present a new model, and talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in triple $b$-metric space. Finally, we give an examples to illustrate our main results.
