Future Scope and Open Problems

Vijay Gupta and Ravi P. Agarwal
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Vijay Gupta: Netaji Subhas Institute of Technology, School of Applied Sciences
Ravi P. Agarwal: Texas A&M University - Kingsville, Department of Mathematics

Chapter Chapter 11 in Convergence Estimates in Approximation Theory, 2014, pp 345-347 from Springer

Abstract: Abstract In 1983, based on two parameters α, β satisfying the conditions 0 ≤ α ≤ β, Stancu [222] proposed a generalization of the classical Bernstein polynomials. In more recent papers, some approximation properties of the Stancu-type generalization on different operators were discussed (see, e.g., [50, 133, 187, 238]). Future studies could address defining the Stancu-type generalization of other operators and the convergence behavior, asymptotic formulas, and rate of convergence for functions of BV and for functions having derivatives of BV.

Keywords: Stancu Type Generalization; Classical Bernstein Polynomials; Approximation Properties; Baskakov Durrmeyer Operators; Mixing Performance (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-02765-4_11

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