Best Simultaneous Approximation in Probabilistic Normed Spaces (original) (raw)

Best approximation in quotient probabilistic normed space

Journal of Applied Analysis

In this article, we study the best approximation in quotient probabilistic normed space. We define the notion of quotient space of a probabilistic normed space, then prove some theorems of approximation in quotient space are extended to quotient probabilistic normed space.

Best p-Simultaneous Approximation in Some Metric Space

DergiPark (Istanbul University), 2008

Let X be a Banach space, (I, µ) be a finite measure space, and Φ be an increasing subadditive continuous function on [0, +∞) with Φ(0) = 0. In the present paper, we discuss the best p-simultaneous approximation of L Φ (I, G) in L Φ (I, X) where G is a closed subspace of X.

Some classes of probabilistic normed spaces

The authors’ abstract: “Probabilistic normed spaces (PN spaces) have recently been redefined by C. Alsina, B. Schweizer, and A. Sklar [Aequationes Math. 46, No. 1-2, 91-98 (1993; Zbl 0792.46062)]. The authors begin the study of these spaces by giving several examples; in particular, they (a) present a detailed study of α-simple spaces, (b) construct a PN space on the vector space of (equivalence classes) of random variables, and (c) show that its probabilistic norm alone generates the norms of all L p - and Orlicz spaces”.

On best simultaneous approximation in quotient spaces

Analysis in Theory and Applications, 2007

We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W + M and the quotient space W /M.

On random coincidence points and random best approximation in p-normed spaces

Mathematical theory and modeling, 2016

In this paper random coincidence point results are proved for pair of commuting mapping defined on weakly compact separable subset of complete p-normed space. And then , use them to study the random best approximation in p-normed space with separablity condition.Keywords : p-normed space ,random coincidence point ,random best approximation.

Best simultaneous approximation on metric spaces via monotonous norms

Filomat, 2020

For a Banach space X, L?(T,X) denotes the metric space of all X-valued ?-integrable functions f : T ? X, where the measure space (T,?,?) is a complete positive ?-finite and ? is an increasing subadditive continuous function on [0,?) with ?(0) = 0. In this paper we discuss the proximinality problem for the monotonous norm on best simultaneous approximation from the closed subspace Y?X to a finite number of elements in X.

Ideal convergent sequences of functions in probabilistic normed spaces

The journal of mathematics and computer science, 2021

In the present article, we have defined the notion of I-pointwise convergence and I-uniform convergence of sequence of functions defined on a probabilistic normed space with respect to the probabilistic norm ν. Further we have given the Cauchy criteria for I-pointwise and I-uniform convergence in PNS. Also, we have proved certain results on continuity of functions with respect to ν in PNS.

New Types of Continuous Linear Operator in Probabilistic Normed Space

Bulletin of the Malaysian Mathematical Sciences Society, 2009

In this paper, new types of continuous linear operator, such as continuous, strongly continuous, weakly continuous and sequentially continuous linear operators, in probabilistic normed space are introduced. Also, the relation between the boundedness and continuity of these linear operators in probabilistic normed spaces is studied.