scholarly journals On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions

1999 ◽  
Vol 136 (3) ◽  
pp. 271-295 ◽  
Author(s):  
Enrico Priola
Keyword(s):  
Markov Type ◽  
Bounded Functions ◽  
Uniformly Continuous

Approximation Par des Fonctions Lipschitziennes et Critere de Convergence Etroite D'une Suite de Probabilites

1984 ◽  
Vol 27 (4) ◽  
pp. 514-516 ◽  
Author(s):  
I. Rihaoui
Keyword(s):  
Weak Convergence ◽  
Metric Space ◽  
Bounded Function ◽  
Uniform Limit ◽  
Bounded Functions ◽  
New Criterion ◽  
Uniformly Continuous

AbstractIn this paper, we prove that a real valued bounded function, defined on a metric space and uniformly continuous is the uniform limit of a sequence of Lipschitzian bounded functions.As a consequence, a new criterion for the weak convergence of probabilities is given.

scholarly journals Linear isometries on subalgebras of uniformly continuous functions

2000 ◽  
Vol 43 (1) ◽  
pp. 139-147 ◽  
Author(s):  
Jesús Araujo ◽  
Juan J. Font
Keyword(s):  
Banach Spaces ◽  
Continuous Functions ◽  
Bounded Functions ◽  
Uniformly Continuous ◽  
Linear Isometries

AbstractWe describe the linear surjective isometries between various subalgebras of uniformly continuous bounded functions defined on closed subsets of Banach spaces.

scholarly journals An Inverse Result of Approximation by Sampling Kantorovich Series

2018 ◽  
Vol 62 (1) ◽  
pp. 265-280 ◽  
Author(s):  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Real Line ◽  
Representation Formula ◽  
Order Of Approximation ◽  
Generalized Sampling ◽  
Representation Formulas ◽  
Sampling Series ◽  
Bounded Functions ◽  
Saturation Theorem ◽  
Uniformly Continuous ◽  
Kantorovich Operators

AbstractIn the present paper, an inverse result of approximation, i.e. a saturation theorem for the sampling Kantorovich operators, is derived in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, we prove that the best possible order of approximation that can be achieved by the above sampling series is the order one, otherwise the function being approximated turns out to be a constant. The above result is proved by exploiting a suitable representation formula which relates the sampling Kantorovich series with the well-known generalized sampling operators introduced by Butzer. At the end, some other applications of such representation formulas are presented, together with a discussion concerning the kernels of the above operators for which such an inverse result occurs.

scholarly journals Uniqueness of invariant means on certain introverted spaces

1973 ◽  
Vol 9 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Marvin W. Grossman
Keyword(s):  
Continuous Functions ◽  
Constant Function ◽  
Invariant Mean ◽  
Closed Convex Hull ◽  
Continuous Multiplication ◽  
Bounded Functions ◽  
Invariant Means ◽  
Closed Invariant Subspace ◽  
Uniformly Continuous ◽  
Uniformly Closed

Let S be a topological semigroup with separately continuous multiplication and H a uniformly closed invariant subspace of LUC(S) (the space of left uniformly continuous bounded functions on S ) that contains the constants. It is shown that if H is left introverted and H admits a tight two-sided invariant mean m, then for each h ∈ H, m(h) is the unique constant function in the norm closed convex hull of the left orbit of h; consequently, H has a unique left invariant mean. (In fact, it is enough for H to admit a tight right invariant mean and a left invariant mean. ) For certain S, a similar result is obtained when H is a left compact-open introverted subspace of LCC(S) (the space of left compact-open continuous functions on S ).

A VECTOR-VALUED VERSION OF RUSSO–DYE THEOREM

2009 ◽  
Vol 11 (06) ◽  
pp. 1035-1048
Author(s):  
J. C. NAVARRO-PASCUAL ◽  
M. G. SÁNCHEZ-LIROLA
Keyword(s):  
Unit Ball ◽  
Convex Combination ◽  
Extreme Points ◽  
Closed Convex Hull ◽  
Real Vector ◽  
Compact Metric Space ◽  
Bounded Functions ◽  
Vector Valued ◽  
Uniformly Continuous ◽  
Extremal Structure

In this paper, we will study the extremal structure of the unit ball of U(M,X), the space of uniformly continuous and bounded functions, from a not necessarily compact metric space M into a normed space X. Concretely, if X is uniformly convex and dim X ≥ 2, where dim X denotes the dimension of X as a real vector space, it is proved that every element y in U(M,X), with ‖y‖ < 1, is a convex combination of a finite number of extreme points of the unit ball. As a result, the unit ball of U(M,X) coincides with the closed-convex hull of its extreme points.

LIFTING THE FUNCTOR ITO THE CATEGORY OF UNIFORM SPACES

2020 ◽  
Vol 4 (1) ◽  
pp. 29-39
Author(s):  
Dilrabo Eshkobilova ◽  
Keyword(s):  
Compact Support ◽  
Probability Measures ◽  
Uniform Spaces ◽  
Continuous Maps ◽  
Uniformly Continuous

Uniform properties of the functor Iof idempotent probability measures with compact support are studied. It is proved that this functor can be lifted to the category Unif of uniform spaces and uniformly continuous maps

scholarly journals Fractional Ostrowski type inequalities for bounded functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Samet Erden ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya ◽  
Sabah Iftikhar ◽  
Poom Kumam
Keyword(s):  
Bounded Functions
Sign in / Sign up

Export Citation Format

Share Document