A Decomposition of the Limit q-Bernstein Type Operators Via a Universal Factor

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2026年1月13日

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Sofiya Ostrovska,
Lütfi Atahan Pirimoğlu,
Mehmet Turan

摘要

The focus of this work is on the properties of the unifying operator $U_q$ $U_{q}$ on C[0, 1], which serves as a universal left factor in a decomposition of the limit q-Bernstein type operators, $L_{\infty ,q}$ $L_{\infty, q}$ . More precisely, the factorization $L_{\infty ,q}= U_q\circ T_L$ $L_{\infty, q} = U_{q} \circ T_{L}$ , where $T_L$ $T_{L}$ is a linear operator on C[0, 1] depending on L, holds. It is shown that this factorization facilitates the derivation of new results and/or the simplification of proofs for the known ones.