How Analytic Properties of Functions Influence Their Images Under the Limit q-Stancu Operator?
Abstract
Abstract In the study of various q -versions of the Bernstein polynomials, a significant attention is paid to their limit operators. The present work focuses on the impact of the limit q -Stancu operator $$S_{\infty }^{q,\alpha }$$ S ∞ q , α on the analytic properties of functions when $$0 0 < q < 1 and $$\alpha >0.$$ α > 0 . It is shown that for every $$f\in C[0,1],$$ f ∈ C [ 0 , 1 ] , the function $$S_{\infty }^{q,\alpha }f$$ S ∞ q , α f admits an analytic continuation into the disk $$\{z: |z+\alpha /(1-q)|
Fields of Study & Subjects
Approximation Theory and Sequence Spaces
Mathematical functions and polynomials
Analytic and geometric function theory
Publication details
- Journal / source
- Mediterranean Journal of Mathematics
- Volume
- 23
- Issue
- 1
- Publication date
- 10 January 2026
- Language
- EN