## $$L_p$$-inverse theorem for modified beta operators.(English)Zbl 1080.41016

Beta operators are linear positive operators defined on $$L_p$$ function spaces of the nonnegative real line. In this paper, an inverse result is established that derives a certain $$L_p$$ modulus of smoothness from the order of approximation that is obtained when using beta operators. For this the approximand must be from $$L_p[0,\infty)$$, the modulus of smoothness is of order $$2k+2$$, and the approximation order is $$\alpha/2$$ with $$0<\alpha<2k+2$$.

### MSC:

 41A25 Rate of convergence, degree of approximation 41A30 Approximation by other special function classes

### Keywords:

inverse theorems; beta operators
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