Akademik Veri Yönetim Sistemi
Filomat, cilt.40, sa.4, ss.1341-1360, 2026 (SCI-Expanded, Scopus)
In this paper, we investigate a generalized Szász–type positive linear operator recently introduced in the literature and analyze its fundamental properties through the study of moments. In particular, we construct several important modifications, namely the Stancu, Kantorovich and Stancu–Kantorovich variants, and derive explicit expressions for their first-and second-order moments. These moment identities provide the basis for establishing various approximation properties of the operators. More specifically, they are instrumental in proving Korovkin-type theorems, estimating rates of convergence via the modulus of continuity and Peetre’s K-functional, and examining approximation behavior in Lipschitz spaces. Further-more, we employ these identities to obtain Voronovskaya-type asymptotic results. The findings presented here contribute to a deeper understanding of the approximation capabilities of generalized Szász–type operators and their modifications, thereby enriching the theory of positive linear operators.