This paper primarily discusses and proves the Hyers–Ulam stability of three types of polynomial equations: x n + a 1 x + a 0 = 0 , a n x n + ⋯ + a 1 x + a 0 = 0 , and the infinite series equation: ∑ i = 0 ∞ a i x i = 0 , in dislocated quasi–metric spaces under certain conditions by constructing contraction mappings and using fixed–point methods. We present an example to illustrate that the Hyers–Ulam stability of polynomial equations in dislocated quasi–metric spaces do not work when the constant term is not equal to zero.

Keywords: dislocated quasi-metric spaces, Hyers-Ulam stability, polynomial equations