Graph-distance convergence and uniform local boundedness of monotone mappings
نویسندگان
چکیده
منابع مشابه
Graph-distance Convergence and Uniform Local Boundedness of Monotone Mappings
In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uni...
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We consider bifunctions F : C ×C → R where C is an arbitrary subset of a Banach space. We show that under weak assumptions, monotone bifunctions are locally bounded in the interior of their domain. As an immediate corollary, we obtain the corresponding property for monotone operators. Also, we show that in contrast to maximal monotone operators, monotone bifunctions (maximal or not maximal) can...
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We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...
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This paper gives sufficient conditions for graphical convergence of sums of maximal monotone mappings. The main result concerns finitedimensional spaces and it generalizes known convergence results for sums. The proof is based on a duality argument and a new boundedness result for sequences of monotone mappings which is of interest on its own. An application to the epi-convergence theory of con...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-07179-x