Search results for "General Mathematics"
showing 10 items of 3795 documents
L -valued bornologies on powersets
2016
In M. Abel and A. ostak (2011) [1], the concept of an L-fuzzy bornology was introduced. Actually, an L-fuzzy bornology on a set X is a certain ideal in the family LX of L-fuzzy subsets of a set X. Here we propose an alternative approach to fuzzification of the concept of bornology. We define an L-valued bornology on a set X as an L-fuzzy subset B of the powerset 2X satisfying L-valued analogues of the axioms of a bornology. Basic properties of L-valued bornological spaces are studied. Our special interest concerns L-valued bornologies induced by fuzzy metrics and relative compactness-type L-valued bornologies in ChangGoguen L-topological spaces.
Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs
2014
In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1. We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient …
About Aczél Inequality and Some Bounds for Several Statistical Indicators
2020
In this paper, we will study a refinement of the Cauchy&ndash
Some fixed point results via R-functions
2016
We establish existence and uniqueness of fixed points for a new class of mappings, by using R-functions and lower semi-continuous functions in the setting of metric spaces. As consequences of this results, we obtain several known fixed point results, in metric and partial metric spaces. An example is given to support the new theory. A homotopy result for operators on a set endowed with a metric is given as application.
Common fixed points for self-mappings on partial metric spaces
2012
Abstract In this paper, we prove some results of a common fixed point for two self-mappings on partial metric spaces. Our results generalize some interesting results of Ilić et al. (Appl. Math. Lett. 24:1326-1330, 2011). We conclude with a result of the existence of a fixed point for set-valued mappings in the context of 0-complete partial metric spaces. MSC:54H25, 47H10.
VECTOR-VALUED FUNCTIONS INTEGRABLE WITH RESPECT TO BILINEAR MAPS
2008
Let $(\Omega, \Sigma, \mu)$ be a $\sigma-$finite measure space, $1\le p \lt \infty$, $X$ be a Banach space $X$ and ${\cal B} :X\times Y \to Z$ be a bounded bilinear map. We say that an $X$-valued function $f$ is $p-$integrable with respect to ${\cal B}$ whenever $\sup\{\int_\Omega\|{\cal B}(f(w),y)\|^pd\mu: \|y\|=1\}$ is finite. We identify the spaces of functions integrable with respect to the bilinear maps arising from H\"older's and Young's inequalities. We apply the theory to give conditions on $X$-valued kernels for the boundedness of integral operators $T_{{\cal B}}(f) (w)=\int_{\Omega'}{{\cal B}}(k(w,w'),$ $f(w'))d\mu'(w')$ from ${\mathrm L}^p(Y)$ into ${\mathrm L}^p(Z)$, extending t…
Generalized quasidisks and conformality II
2015
We introduce a weaker variant of the concept of three point property, which is equivalent to a non-linear local connectivity condition introduced in [12], sufficient to guarantee the extendability of a conformal map f from the unit disk onto a domain to the entire plane as a homeomorphism of locally exponentially integrable distortion. Sufficient conditions for extendability to a homeomorphism of locally p-integrable distortion are also given.
A decomposition theorem for compact-valued Henstock integral
2006
We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ.
An integral representation for decomposable measures of measurable functions
1994
We start with a measurem on a measurable space (Ω,A), decomposable with respect to an Archimedeant-conorm ⊥ on a real interval [0,M], which generalizes an additive measure. Using the integral introduced by the second author, a Radon-Nikodym type theorem, needed in what follows, is given.
Polynomial identities with involution, superinvolutions and the Grassmann envelope
2017
Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.