The characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of Rn. Similar results are obtained for little Bloch and Besov spaces.

The purpose of this paper is to prove common fixed point theorem for four mappings without continuity and compatibility on intuitionistic fuzzy metric space.

We study a topology on a space of functions, called sticking topology, with the property to be the weakest among the topologies preserving continuity. In suitable frameworks, this topology preserves borelianity, local integrability, right continuity and other properties. It is coarser than the locally uniform convergence and it allows the presence of gliding humps as we show on examples. We pro...

In this note we show that in a certain subfamily of the Kuranishi family of any half Inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semi-continuity of algebraic dimensions in any sense does not hold in general for families of compact non-Kähler manifolds. In the Kähler case, the upper semi-continuity always hol...

Brownian motions in the innnite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent one-dimensional Brownian motions. The proof involves continuous tensor products and continuous quantum measurements. A by-product: a Brownian motion in a separab...

As application of complete metric space, we proved a Baire’s category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we showed some topological properties of two spaces, which are topological space and linear topological space ge...

The intent of this paper is to extend the notions of occasionally weakly compatible mappings, subcompatibility and subsequential continuity in framework of generalized metric spaces and prove some common fixed point theorems. We give some examples which demonstrate the validity of the hypotheses and degree of generality of our results. Our results are independent of the continuity requirement o...

We study families of time-varying linear systems, where time-variations have to satisfy restrictions on the dwell time, that is, on the minimum distance between discontinuities, as well as on the derivative in between discontinuities. For this class of systems we study continuity properties of the growth rate as a function of the systems’ data. It is shown by example, that a straightforward top...

This paper examines the control continuity in hierarchical task-space controllers. While the continuity is ensured for any a priori fixed number of tasks –even in ill-conditioned configurations–, the control resulting from a hierarchical stack-of-task computation may not be continuous under some discrete events. In particular, we study how the continuity of the stack-of-task control computation...

We study adaptive estimation of linear functionals over a collection of finitely many parameter spaces.A between class modulus of continuity, a geometric quantity, is introduced and is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single par...