Beta operators with Jacobi weights
Heiner Gonska, Ioan Ra\c{s}a, Elena Dorina St\u{a}nil\u{a}
TL;DR
This paper studies Beta operators with Jacobi weights on continuous functions, analyzing their moments, asymptotic behavior, and over-iteration effects, including limiting cases and Voronovskaya-type results.
Contribution
It introduces a comprehensive analysis of Beta operators with Jacobi weights, including moments, asymptotics, and over-iteration, covering limiting cases.
Findings
Detailed moments and asymptotic behavior characterized
Extended Voronovskaya-type theorems established
Insights into over-iteration effects provided
Abstract
We discuss Beta operators with Jacobi weights on for , thus including the discussion of three limiting cases. Emphasis is on the moments and their asymptotic behavior. Extended Voronovskaya-type results and a discussion concerning the over-iteration of the operators are included.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Holomorphic and Operator Theory · Mathematical Analysis and Transform Methods