Investigating the Quantitative Behavior of Kantorovich Fractional Operators in q-Numbers
DOI:
https://doi.org/10.65135/atsf.2026.14Keywords:
Modulus of continuity, rate of convergence, q-calculus, Voronovskaya approximation, weighted approximationAbstract
This research introduces the Kantorovich-type fractional Baskakov operators defined via q-integers and investigates their approximation properties. We compute the moments and central moments of these operators and establish Korovkin-type approximation theorems along with estimates of their rate of convergence. The analysis is carried out using tools such as the Lipschitz class, Lipschitz-type maximal functions, Peetre's K-functional, and the first- and second-order moduli of smoothness. Furthermore, a Voronovskaya-type theorem is proved, and the weighted approximation properties of the operators are examined. Finally, a numerical comparison of the proposed operators is presented, supported by graphical illustrations.
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