论文信息 - An answer to Hermann's conjecture on Bleimann-Butzer-Hahn operators

An answer to Hermann's conjecture on Bleimann-Butzer-Hahn operators

We give a negative answer to the conjecture of Hermann [On the operator of Bleimann, Butzer and Hahn, in: J. Szabados, K. Tandori (Eds.), Approximation Theory, Proc. Conf., Kecskemet/Hung., 1990, North-Holland Publishing Company, Amsterdam, 1991, Colloq. Math. Soc. Janos Bolyai 58 (1991) 355-360] on Bleimann-Butzer-Hahn operators L"n. Our main result states that for each locally bounded positive function h there exists a continuous positive function f defined on [0,~) with L"nf->f(n->~), pointwise on [0,~), such thatlimsupx->+~f(x)h(x)=+~.Moreover we construct an explicit counterexample function to Hermann's conjecture.

Ulrich Abel | Mircea Ivan | U. Abel | M. Ivan

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