In this paper, (p, q)-Bernstein bases and operators are constructed over arbitrary compact intervals. Due to the property that these bases are scale invariant but not translation invariant, the derived results on arbitrary intervals are important from computational aspects. Approximation properties of (p, q)-Bernstein operators on arbitrary compact intervals [a, b] where \(b>a\ge 0\) for \(0<q<p<\infty \) based on Korovkin-type theorem are investigated. Rate of convergence by modulus of continuity and functions of Lipschitz class are computed. Graphical representations are added to demonstrate consistency to theoretical findings for the operators approximating functions.

在本文中，( p ,  q )-Bernstein 基和算子是在任意紧凑区间上构造的。由于这些基是尺度不变的但不是平移不变的，因此从计算方面来看，任意间隔上的派生结果很重要。( p ,  q )-Bernstein 算子在任意紧凑区间 [ a ,  b ]上的近似性质，其中\(b>a\ge 0\) for \(0<q<p<\infty \)基于 Korovkin 型定理进行了研究。计算通过连续性模数和 Lipschitz 类函数的收敛速度。添加了图形表示以证明与算子逼近函数的理论结果的一致性。