Mahmudov, N. I.; Sabancıgil, P. \(q\)-parametric Bleimann Butzer and Hahn operators. (English) Zbl 1154.41012 J. Inequal. Appl. 2008, Article ID 816367, 15 p. (2008). Let the \(q\)-Bernstein polynomials are given by \[ B_{n,q}(f)(x) := \sum^n_{k=0}f \left({[k]\over[n]} \right) {n\choose k} \, x^k \prod^{n-k-1}_{s=0} (1-q^sx). \] In this paper, a \(q\)-analog of the Bleimann, Butzer and Hahn operators of the form \[ H_{n,q}(f)(x) := (\Phi^{-1}B_{n+1,q}\, \Phi)(f) (x) \] is proposed, where \( \Phi : C^*_p [0,\infty) \to C[0,1]\) is a suitable positive linear isomorphism. The authors study the properties of the \(q\)-BBH operators \(H_{n,q} \) and establish the rate of convergence. A Voronovskaja-type theorem and saturation of convergence for \(q\)-BBH operators for \( 0 < q < 1\) is discussed. Further, the convergence of the derivative of \(q\)-BBH operators is considered. Reviewer: Gerlind Plonka (Duisburg) Cited in 8 Documents MSC: 41A36 Approximation by positive operators 41A40 Saturation in approximation theory 41A25 Rate of convergence, degree of approximation Keywords:rate of convergence; Voronovskaja-type theorem; saturation of convergence PDF BibTeX XML Cite \textit{N. I. Mahmudov} and \textit{P. Sabancıgil}, J. Inequal. Appl. 2008, Article ID 816367, 15 p. (2008; Zbl 1154.41012) Full Text: DOI References: [3] doi:10.1023/B:BITN.0000025086.89121.d8 · Zbl 1045.41003 · doi:10.1023/B:BITN.0000025086.89121.d8 [5] doi:10.1016/j.amc.2007.07.056 · Zbl 1142.41008 · doi:10.1016/j.amc.2007.07.056 [6] doi:10.1016/j.amc.2007.04.085 · Zbl 1128.33014 · doi:10.1016/j.amc.2007.04.085 [7] doi:10.1007/s10092-006-0119-3 · Zbl 1121.41016 · doi:10.1007/s10092-006-0119-3 [9] doi:10.1016/j.jmaa.2007.01.103 · Zbl 1129.41010 · doi:10.1016/j.jmaa.2007.01.103 [16] doi:10.1006/jmaa.1997.5371 · Zbl 0872.41009 · doi:10.1006/jmaa.1997.5371 [17] doi:10.1006/jath.1997.3253 · Zbl 0928.41012 · doi:10.1006/jath.1997.3253 [18] doi:10.1016/0021-9045(88)90024-X · Zbl 0676.41024 · doi:10.1016/0021-9045(88)90024-X [19] doi:10.1155/2007/79410 · Zbl 1133.41001 · doi:10.1155/2007/79410 [21] doi:10.1016/j.jat.2005.07.001 · Zbl 1082.41007 · doi:10.1016/j.jat.2005.07.001 [22] doi:10.1006/jath.2001.3657 · Zbl 0999.41007 · doi:10.1006/jath.2001.3657 [23] doi:10.1016/j.jat.2006.08.005 · Zbl 1112.41016 · doi:10.1016/j.jat.2006.08.005 [24] doi:10.1007/3-7643-7340-7_15 · doi:10.1007/3-7643-7340-7_15 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.