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<p>This paper investigates Korovkin-type approximation results for double sequences of monotone and sublinear operators under power series summability methods. We introduce a double-sequence analogue that extends existing one-dimensional nonlinear Korovkin results. We first establish convergence criteria and derive the corresponding rates of approximation in terms of the modulus of continuity. To illustrate the applicability of the theory, we construct a double-sequence version of the Bernstein–Chlodovsky–Kantorovich–Choquet (BCKC) operators by <i>RH</i>-regular methods, together with additional examples satisfying the required conditions. These results indicate that power series methods are effective in the analysis of nonlinear double operator sequences in Korovkin-type settings.</p>

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Korovkin Theory via Power Series Methods for Double Sequences of Monotone Sublinear Operators

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  • 发表日期：

    2026年6月16日

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摘要

This paper investigates Korovkin-type approximation results for double sequences of monotone and sublinear operators under power series summability methods. We introduce a double-sequence analogue that extends existing one-dimensional nonlinear Korovkin results. We first establish convergence criteria and derive the corresponding rates of approximation in terms of the modulus of continuity. To illustrate the applicability of the theory, we construct a double-sequence version of the Bernstein–Chlodovsky–Kantorovich–Choquet (BCKC) operators by RH-regular methods, together with additional examples satisfying the required conditions. These results indicate that power series methods are effective in the analysis of nonlinear double operator sequences in Korovkin-type settings.