article.page.titleprefix On the continuity in q of the family of the limit q-Durrmeyer operators
| dc.contributor.author | Gürel Yılmaz, Övgü | |
| dc.contributor.author | Ostrovska, Sofiya | |
| dc.contributor.author | Turan, Mehmet | |
| dc.date.accessioned | 2024-05-03T11:35:13Z | |
| dc.date.available | 2024-05-03T11:35:13Z | |
| dc.date.issued | 2024-04-25 | |
| dc.description | Open Access; Published by Demonstratio Mathematica; https://doi.org/10.1515/dema-2023-0157; Övgü Gürel Yılmaz, Recep Tayyip Erdogan University, Department of Mathematics, 53100, Rize, Turkey; Sofiya Ostrovska, Mehmet Turan, Atilim University, Department of Mathematics, Incek 06830, Ankara, Turkey. | |
| dc.description.abstract | The present paper deals with the one-parameter family {Dq}q∈[0,1] 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 {Dq}q∈[0,1] 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]. | |
| dc.identifier.citation | https://hdl.handle.net/20.500.14411/2028 | |
| dc.identifier.issn | 2391-4661 | |
| dc.identifier.uri | https://doi.org/10.1515/dema-2023-0157 | |
| dc.language.iso | en | |
| dc.publisher | Demonstratio Mathematica | |
| dc.relation.ispartofseries | 57; 1 | |
| dc.subject | q-Durrmeyer operator | |
| dc.subject | q-Bernstein-operator | |
| dc.subject | operator norm | |
| dc.subject | strong operator topology | |
| dc.subject | uniform operator topology | |
| dc.subject | 47B38 | |
| dc.subject | 41A36 | |
| dc.title | On the continuity in q of the family of the limit q-Durrmeyer operators | |
| dc.type | Article | |
| dspace.entity.type | Article |