On the modified beta approximating operators of first kind

Authors

  • Vasile Miheşan Technical University of Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat331-760

Keywords:

Euler's beta function, the modified beta first kind operator, positive linear operators
Abstract views: 184

Abstract

We define a general linear operator from which we obtain as special case the modified beta first kind operator\[(B_{p,q}f)(x)={B(p,q)}\int_0^1 t^{p-1}(1-t)^{q-1}f\left({B(p,q)}{B(p+a,q)}t^a x\right){\rm d}t.\]We consider here only the cases \(a=1\) and \(a=-1\).We obtain several positive linear operators as particular cases of this modified beta first kind operator.

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References

Adell, J. A., Badia, F. G., De la Cal, J. and Plo, L., On the property of monotonic convergence for Beta operators, J. Approx. Theory, 84, pp. 61-73, 1996,https://doi.org/10.1006/jath.1996.0005 DOI: https://doi.org/10.1006/jath.1996.0005

Lupaş, A., Die folge der Beta operatoren, Dissertation, Univ. Stuttgart, Stuttgart, 1972.

Miheşan, V., The beta approximating operators of the first kind, Studia Univ. Babeş-Bolyai, Mathematica (to appear).

Miheşan, V., Approximation of continuous functions by means of linear positive operators, PhD Thesis, "Babeş-Bolyai" University, Faculty of Mathematics and Computer Science, Cluj-Napoca, 1997.

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Published

2004-02-01

How to Cite

Miheşan, V. (2004). On the modified beta approximating operators of first kind. Rev. Anal. Numér. Théor. Approx., 33(1), 67–71. https://doi.org/10.33993/jnaat331-760

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