Search results for "A2"
showing 10 items of 1101 documents
On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with L1 Data
2007
We establish Holder continuity of generalized solutions of the Dirichlet problem, associated to a degenerate nonlinear fourth-order equation in an open bounded set , with data, on the subsets of where the behavior of weights and of the data is regular enough.
Unitary Groups Acting on Grassmannians Associated with a Quadratic Extension of Fields
2006
Let (V, H) be an anisotropic Hermitian space of finite dimension over the algebraic closure of a real closed field K. We determine the orbits of the group of isometries of (V, H) in the set of K-subspaces of V . Throughout the paper K denotes a real closed field and K its algebraic closure. Then it is well known (see, for example, [4, Chapter 2], [23]; see also [8]) that K = K(i) with i = √−1. Also we let (V,H) be an anisotropic Hermitian space (with respect to the involution underlying the quadratic field extension K/K) of finite dimension n over K. In this context we consider the natural action of the unitary group U = U(V,H) of isometries of (V,H) on the set Xd of all ddimensional K-subs…
Introduction to generalized topological spaces
2011
[EN] We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.
Fuzzy functions: a fuzzy extension of the category SET and some related categories
2000
<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -&gt; L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>
Fixed point and homotopy results for mixed multi-valued mappings in 0-complete partial metric spaces*
2015
We give sufficient conditions for the existence of common fixed points for a pair of mixed multi-valued mappings in the setting of 0-complete partial metric spaces. An example is given to demonstrate the usefulness of our results over the existing results in metric spaces. Finally, we prove a homotopy theorem via fixed point results.
JH-Operators and Occasionally Weakly g-Biased Pairs in Fuzzy Symmetric Spaces
2013
We introduce the notions of $\mathcal{JH}$-operators and occasionally weakly $g$-biased mappings in fuzzy symmetric spaces to prove common fixed point theorems for self-mappings satisfying a generalized mixed contractive condition. We also prove analogous results for two pairs of $\mathcal{JH}$-operators by assuming symmetry only on the set of points of coincidence. These results unify, extend and complement many results existing in the recent literature. We give also an application of our results to product spaces.
Quasi-pseudometric properties of the Nikodym-Saks space
2003
[EN] For a non-negative finite countably additive measure μ defined on the σ-field Σ of subsets of Ω, it is well known that a certain quotient of Σ can be turned into a complete metric space Σ (Ω), known as the Nikodym-Saks space, which yields such important results in Measure Theory and Functional Analysis as Vitali-Hahn-Saks and Nikodym's theorems. Here we study some topological properties of Σ (Ω) regarded as a quasi-pseudometric space.
A Note on Algebraic Sums of Subsets of the Real Line
2002
AbstractWe investigate the algebraic sums of sets for a large class of invari-ant ˙-ideals and ˙- elds of subsets of the real line. We give a simpleexample of two Borel subsets of the real line such that its algebraicsum is not a Borel set. Next we show a similar result to Proposition 2from A. Kharazishvili paper [4]. Our results are obtained for ideals withcoanalytical bases. 1 Introduction We shall work in ZFC set theory. By !we denote natural numbers. By 4wedenote the symmetric di erence of sets. The cardinality of a set Xwe denoteby jXj. By R we denote the real line and by Q we denote rational numbers. IfAand Bare subsets of R n and b2R , then A+B= fa+b: a2A^b2Bgand A+ b= A+ fbg. Simila…
Internal inverse limits and retractions
2015
We establish equivalences between compacta that admit a sequence of retractions that converge uniformly to the identity map and compacta that are inverse limits on subcompacta with retractions for bonding maps. We give partial answers to questions of Charatonik and Prajs, and of Krasinkiewicz. Our results are related to and use results from another paper of the authors \cite{mp}.
Impact of common property (E.A.) on fixed point theorems in fuzzy metric spaces
2011
We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.