If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we...If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.展开更多
We give a neccesary and sufficient condition on a function such that the composition operator (Nemytskij Operator) H defined by acts in the space and satisfies a local Lipschitz condition. And, we prove that ever...We give a neccesary and sufficient condition on a function such that the composition operator (Nemytskij Operator) H defined by acts in the space and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener p(·)-variation with variable exponent functions into itself is a Nemytskij com-position operator.展开更多
文摘If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.
文摘We give a neccesary and sufficient condition on a function such that the composition operator (Nemytskij Operator) H defined by acts in the space and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener p(·)-variation with variable exponent functions into itself is a Nemytskij com-position operator.
