On the continuity in q of the family of the limit q-Durrmeyer operators

• Autorzy: Yılmaz Övgü Gürel , Ostrovska Sofiya , Turan Mehmet

Identyfikatory

DOI

10.1515/dema-2023-0157

• Języki publikacji: EN

Abstrakty

EN

This study deals with the one-parameter family […] of Bernstein-type operators introduced by Gupta and called the limit q-Durrmeyer operators. The continuity of this family with respect to the parameter q is examined in two most important topologies of the operator theory, namely, the strong and uniform operator topologies. It is proved that […] is continuous in the strong operator topology for all q ∈ [0,1]. When it comes to the uniform operator topology, the continuity is preserved solely at q = 0 and fails at all q ∈ (0,1]. In addition, a few estimates for the distance between two limit q-Durrmeyer operators have been derived in the operator norm on C[0,1].

Słowa kluczowe

EN

q-Durrmeyer operator; q-Bernstein operator; operator norm; strong operator topology; uniform operator topology

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20230157
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Yılmaz Övgü Gürel

• Department of Mathematics, Recep Tayyip Erdogan University, 53100, Rize, Turkey

autor

Ostrovska Sofiya

• Department of Mathematics, Atilim University, Incek 06830, Ankara, Turkey

autor

Turan Mehmet

• Department of Mathematics, Atilim University, Incek 06830, Ankara, Turkey

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).