نتایج جستجو برای: random normed spaces

تعداد نتایج: 411877  

2010
H. AZADI Themistocles M. Rassias

Recently, in [5], Najati and Moradlou proved Hyers-Ulam-Rassias stability of the following quadratic mapping of Apollonius type Q(z − x) + Q(z − y) = 1 2 Q(x− y) + 2Q ( z − x + y 2 ) in non-Archimedean space. In this paper we establish Hyers-Ulam-Rassias stability of this functional equation in random normed spaces by direct method and fixed point method. The concept of Hyers-Ulam-Rassias stabi...

Journal: :Formalized Mathematics 2014
Kazuhisa Nakasho Yuichi Futa Yasunari Shidama

In this article, we formalize topological properties of real normed spaces. In the first few parts, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. In the middle of the article, we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, ima...

Journal: :mathematics interdisciplinary research 0
toshikazu abe niigata university, japan

in this paper, we consider a generalization of the real normed spaces and give some examples.

2014
Vatan KARAKAYA Necip ŞİMŞEK Müzeyyen ERTÜRK Faik GÜRSOY

In this work, our purpose is to introduce I−convergence of sequences of functions in intuitionistic fuzzy normed space by combining the I−convergence, the sequences of functions and the intuitionistic fuzzy normed spaces, and to investigate relations among concepts such as I−convergence, statistical convergence and the usual convergence of sequences of functions in intuitionistic fuzzy normed s...

Journal: :Formalized Mathematics 2015
Keiko Narita Noboru Endou Yasunari Shidama

In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real ...

Journal: :Hacettepe journal of mathematics and statistics 2023

In probability theory, uniform integrability of families random variables or elements plays an important role in the mean convergence. this paper, we introduce a new version for sequences normed spaces weak sense. We study relationship concept with summability theory by considering statistical also define type taking values topological vector integrals. Moreover, connection as well.

Journal: :iranian journal of science and technology (sciences) 2008
k. haghnejad azar

we introduce some new concepts of topological spaces which say α − separable topologicalspace and o-topological group, α − first axiom, α − second axiom, and we find some relations betweenthem with some applications in normed spaces.

Journal: :Formalized Mathematics 2013

2005
REZA SAADATI MASSOUD AMINI Reza Saadati Massoud Amini

In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion of Dcompactness and D-boundedness in probabilistic normed spaces.

2010
CHRISTOPHER HEIL Christopher Heil

Definition 1.3 (Banach Spaces). It is easy to show that any convergent sequence in a normed linear space is a Cauchy sequence. However, it may or may not be true in an arbitrary normed linear space that all Cauchy sequences are convergent. A normed linear space X which does have the property that all Cauchy sequences are convergent is said to be complete. A complete normed linear space is calle...

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