On the Continuity in <i>q</I> of the Family of the Limit <i>q</I>-durrmeyer Operators
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Date
2024
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de Gruyter Poland Sp Z O O
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Abstract
This study deals with the one-parameter family {D-q}(q is an element of[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 {D-q}(q is an element of[0,1]) is continuous in the strong operator topology for all q is an element of [0, 1]. When it comes to the uniform operator topology, the continuity is preserved solely at q = 0 and fails at all q is an element of (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].
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q-Durrmeyer operator, q-Bernstein operator, operator norm, strong operator topology, uniform operator topology
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Volume
57
Issue
1