A Study on Affine Invariance in ψ-Modified Szász-Kantorovich Operators

Hüseyin Aktuğlu and Mustafa Kara

Journal of Mathematics, 2026, vol. 2026, 1-13

Abstract: In this paper, we propose and analyze a modified class of -ψ Szász–Mirakjan–Kantorovich operators that preserve affine functions. The proposed modified-ψ Szász–Mirakjan–Kantorovich operators exhibit superior approximation properties compared to both the classical ψ Szász–Mirakjan–Kantorovich operators and the previously defined -ψ Szász–Mirakjan–Kantorovich operators. The local and direct approximation properties of the proposed operators are examined in detail. Furthermore, we analyze their weighted approximation behavior in terms of the modulus of continuity and establish several Voronovskaja-type theorems for these operators. In addition, the bivariate extension of the proposed operators is introduced, and its approximation properties are studied. Moreover, the approximation performance of both the univariate and bivariate -ψ Szász–Mirakjan–Kantorovich operators are illustrated through graphical representations. Finally, the modeling capabilities of the newly modified operators are demonstrated on the global carbon dioxide emissions example.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6697212

DOI: 10.1155/jom/6697212

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