AbstractIn this paper we introduce a property and use this property to prove some common fixed point theorems inb-metric space. We also give some fixed point results onb-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) = ∫abK1 (t,r,x(r)) dr,x (t) = ∫abK2 (t,r,x(r)) dr,     $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,} $$wherea, b∈ ℝ witha<b, x∈C[a, b] (the set of continuous real functions defined on [a, b] ⊆ ℝ) andK1,K2: [a, b] × [a, b] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.