This research introduces a new fractional integral operator connected to Charlier polynomials, demonstrating significant approximation properties and convergence behavior.
The goal of this manuscript is to introduce a new Stancu generalization of the modified Szász–Kantorovich operator connecting Riemann–Liouville fractional operators via Charlier polynomials. Further, some estimates are calculated as test functions and central moments. In the next section, we investigate some convergence analysis along with the rate of approximations. Moreover, we discuss the order of approximation of a higher-order modulus of smoothness with the help of some moments and establish some convergence results concerning Peetre’s K-functional, Lipschitz-type functions for a newly developed operator SKn+p,av1,v2. We estimate some results related to Korovkin-, Voronovskaya-, and Grüss–Voronovskaya-type theorems.
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Rao et al. (2025) studied this question.
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