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In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) =  ∫ a b K 1  (t,r,x(r)) dr, x (t) =  ∫ a b K 2  (t,r,x(r)) dr,       $$x\left(t\right)=\underset{a}{\overset{b}{\int }}{K}_1(t,r,x\left(r\right))dr,x\left(t\right)=\underset{a}{\overset{b}{\int }}{K}_2(t,r,x\left(r\right))dr,$$ where a, b...