Search results for "Complete"

Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces

2012

Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004…

The convolution operation on the spectra of algebras of symmetric analytic functions

2012

Abstract We show that the spectrum of the algebra of bounded symmetric analytic functions on l p , 1 ≤ p + ∞ with the symmetric convolution operation is a commutative semigroup with the cancellation law for which we discuss the existence of inverses. For p = 1 , a representation of the spectrum in terms of entire functions of exponential type is obtained which allows us to determine the invertible elements.

Multi-valued $$F$$ F -contractions in 0-complete partial metric spaces with application to Volterra type integral equation

2013

We study the existence of fixed points for multi-valued mappings that satisfy certain generalized contractive conditions in the setting of 0-complete partial metric spaces. We apply our results to the solution of a Volterra type integral equation in ordered 0-complete partial metric spaces.

L-fuzzy syntopogenous structures, Part I: Fundamentals and application to L-fuzzy topologies, L-fuzzy proximities and L-fuzzy uniformities

2013

Abstract We introduce the concept of an L-fuzzy syntopogenous structure where L is a complete lattice endowed with an implicator ↦ : L × L → L satisfying certain properties (in particular, as L one can take an MV-algebra). As special cases our L-fuzzy syntopogenous structures contain classical Csaszar syntopogenous structures, Katsaras–Petalas fuzzy syntopogenous structures as well as fuzzy syntopogeneous structures introduced in the previous work of the second named author (A. Sostak, Fuzzy syntopogenous structures, Quaest. Math. 20 (1997) 431–461). Basic properties of the category of L-fuzzy syntopogenous spaces are studied; categories of L-fuzzy topological spaces, L-fuzzy proximity spac…

VECTOR MEASURES WITH VARIATION IN A BANACH FUNCTION SPACE

2003

Let E be a Banach function space and X be an arbitrary Banach space. Denote by E(X) the Kothe-Bochner function space defined as the set of measurable functions f : Ω → X such that the nonnegative functions ‖f‖X : Ω → [0,∞) are in the lattice E. The notion of E-variation of a measure —which allows to recover the pvariation (for E = Lp), Φ-variation (for E = LΦ) and the general notion introduced by Gresky and Uhl— is introduced. The space of measures of bounded E-variation VE(X) is then studied. It is shown, among other things and with some restriction of absolute continuity of the norms, that (E(X))∗ = VE′ (X ∗), that VE(X) can be identified with space of cone absolutely summing operators fr…

Some fixed point results for multi-valued mappings in partial metric spaces

2013

Abstract In this paper, we obtain some fixed point results for multi-valued mappings in partial metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. An example is also included to illustrate the main result in the paper. MSC:46S40, 47H10, 54H25.

On the stability of the Bohl — Brouwer — Schauder Theorem

1996

Countably compact weakly Whyburn spaces

2015

The weak Whyburn property is a generalization of the classical sequential property that was studied by many authors. A space X is weakly Whyburn if for every non-closed set \({A \subset X}\) there is a subset \({B \subset A}\) such that \({\overline{B} \setminus A}\) is a singleton. We prove that every countably compact Urysohn space of cardinality smaller than the continuum is weakly Whyburn and show that, consistently, the Urysohn assumption is essential. We also give conditions for a (countably compact) weakly Whyburn space to be pseudoradial and construct a countably compact weakly Whyburn non-pseudoradial regular space, which solves a question asked by Angelo Bella in private communica…

Minimum node weight spanning trees searching algorithm for broadcast transmission in sensor networks

2017

A minimum node weight spanning tree in a weighted, directed graph is a tree whose node with maximum out-weight is minimal among all spanning trees. This type of trees are important because they appear in the solutions of the maximum lifetime broadcasting problem in wireless sensor networks. In a complete graph build of N nodes there are NN-2 spanning trees and to find such trees it is necessary to perform more than O(NN-2) operations. In this paper we propose an algorithm for searching the minimum node weight spanning trees in the graph. In the proposed algorithm, instead of calculating the symbolic determinant of the generalized Laplacian matrix, numerical operations on its exponents are p…

Orlicz–Sobolev extensions and measure density condition

2010

Abstract We study the extension properties of Orlicz–Sobolev functions both in Euclidean spaces and in metric measure spaces equipped with a doubling measure. We show that a set E ⊂ R satisfying a measure density condition admits a bounded linear extension operator from the trace space W 1 , Ψ ( R n ) | E to W 1 , Ψ ( R n ) . Then we show that a domain, in which the Sobolev embedding theorem or a Poincare-type inequality holds, satisfies the measure density condition. It follows that the existence of a bounded, possibly non-linear extension operator or even the surjectivity of the trace operator implies the measure density condition and hence the existence of a bounded linear extension oper…