Abstract
The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$
α
s
-admissible, triangular partially triple weakly $\alpha _{s}$
α
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, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.