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On simultaneous approximation by summation-integral type Beta operator | ||
| basrah journal of science | ||
| Article 1, Volume 31, Issue 1, 2013, Pages 41-53 PDF (0 K) | ||
| Author | ||
| Abstract | ||
| In this paper, we introduced modified summation-integral Beta operator R_(n,r)^ (f;x) in the space C_α^r of r-times differentiable functions. The definition of these operators is closely connected with considered functional space. we studied simultaneous approximation for a new sequence of linear positive operator R_(n,r)^ (f;x). First, we establish the basic pointwise convergence theorem and the proceed to discuss the Voronovsicoskaja type asymptotic formula. Finally, we obtain an error estimate in terms of modulus of continuity of the function being approximated. | ||
| Keywords | ||
| Approximation by Linear Positive Operators; Voronovsicokaja Theorem; Pointwise Estimate; Simultaneous Approximation | ||
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