Results 1 to 10 of about 10,557 (219)

Normed Ordered and 𝐸-Metric Spaces [PDF]

International Journal of Mathematics and Mathematical Sciences, 2012
In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space 𝐸, and we discuss some properties and examples. Also, normed ordered space is introduced.
Ahmed Al-Rawashdeh, Wasfi Shatanawi, Muna Khandaqji   +2 more
doaj   +3 more sources

Bochner integrals in ordered vector spaces. [PDF]

Positivity (Dordr), 2017
We present a natural way to cover an Archimedean directed ordered vector space $E$ by Banach spaces and extend the notion of Bochner integrability to functions with values in $E$.
van Rooij ACM, van Zuijlen WB.
europepmc   +5 more sources

Monotonic norms in ordered Banach spaces [PDF]

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1988
AbstractLet B be an ordered Banach space with ordered Banach dual space. Let N denote the canonical half-norm. We give an alternative proof of the following theorem of Robinson and Yamamuro: the norm on B is α-monotone (α ≥ 1) if and only if for each f in B* there exists g ∈ B* with g ≥ 0, f and ∥g∥ ≤ α N(f).
Ng, K. F., Law, C. K.
openaire   +2 more sources

An investigation of fractional Bagley-Torvik equation

Open Mathematics, 2019
In this paper the authors prove the existence as well as approximations of the solutions for the Bagley-Torvik equation admitting only the existence of a lower (coupled lower and upper) solution.
Fazli Hossein, Nieto Juan J.
doaj   +1 more source

Coupled fixed point theorems with applications to fractional evolution equations

Advances in Difference Equations, 2017
In this paper, we first prove some coupled fixed point theorems in partially ordered Φ-orbitally complete normed linear spaces. And then apply the obtained fixed point theorems to a class of semilinear evolution systems of fractional order for proving ...
He Yang, Ravi P Agarwal, Hemant K Nashine   +2 more
doaj   +1 more source

A unified theory of cone metric spaces and its applications to the fixed point theory [PDF]

, 2011
In this paper we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory we present full statements of the iterated contraction principle and the Banach contraction principle in cone metric spaces ...
Proinov, Petko D.
core   +2 more sources

Lower semi-continuous regularization of mappings in partially ordered by cone normed spaces

Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ, 2009
The scheme of the lower semi-continuous regularization of mappings in normed spaces is proposed. We make no assumptions on the interior of the ordering cone.
A. V. Dovzhenko
doaj   +1 more source

Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations

Abstract and Applied Analysis, 2014
Some hybrid fixed point theorems of Krasnosel’skii type, which involve product of two operators, are proved in partially ordered normed linear spaces.
H. M. Srivastava, Sachin V. Bedre, S. M. Khairnar, B. S. Desale   +3 more
doaj   +1 more source

Operator system structures on ordered spaces [PDF]

, 2009
Given an Archimedean order unit space (V,V^+,e), we construct a minimal operator system OMIN(V) and a maximal operator system OMAX(V), which are the analogues of the minimal and maximal operator spaces of a normed space.
Paulsen, Vern, Todorov, Ivan, Tomforde, Mark   +2 more
core   +1 more source

Nonstandard hulls of lattice-normed ordered vector spaces

TURKISH JOURNAL OF MATHEMATICS, 2018
Nonstandard hulls of a vector lattice were introduced and studied in \cite{E10,E9,E7,E5,E3}. In recent paper \cite{EG}, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space \cite{E8}, we describe and investigate nonstandard hull of a lattice-normed space, which is ...
Aydin, A., Gorokhova S., Gül H.
openaire   +5 more sources