In this paper, A-statistical approximation of Lupaş (p, q)-Bernstein-Kantorovich operators based on Riemann type integrals for \(1\le q<p<\infty\) is discussed. This work extends the research conducted by Iliyas et al. (Filomat 36(15):5221–5240, 2022; 10.2298/FIL2215221I) on Lupaş (p, q)-Bernstein-Kantorovich operators based on Jackson and Riemann-type integrals for \(1\le q<p<\infty .\) We also emphasize the convergence condition for this sequence of operators for \(1\le q<p<\infty\) and investigate the convergence estimate for the functions by these operators. In this study, both A-statistical convergence theorems and the corresponding rates of A-statistical convergence are established. These results are derived using the notions of A-statistical convergence, the rate of A-statistical convergence, and the modulus of smoothness. Additionally, we present an example showing that while the Lupaş Bernstein-Kantorovich operators, constructed via Riemann-type (p, q)-integrals, exhibit statistical convergence to \(\mathcal {F}(x)\) , the classical Korovkin theorem does not hold in the conventional sense. In this work, we also employ the concept of statistical convergence to approximate all strictly monotonic positive functions \(\mathcal {F} \in \mathcal {C}[0,1]\) using the Lupaş Bernstein-Kantorovich operators constructed through the Jackson integral. Graphical analysis highlighting convergence and flexibility presented for theoretical consistency.
